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Gravitational Physics: Exploring the Structure of Space and Time (1999)

Chapter: 3 Achievements and Opportunities in Gravitational Physics

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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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Suggested Citation:"3 Achievements and Opportunities in Gravitational Physics." National Research Council. 1999. Gravitational Physics: Exploring the Structure of Space and Time. Washington, DC: The National Academies Press. doi: 10.17226/9680.
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~ Achievements an] Opportunities in ~ravitationat Physics I~ G~L wins Key Questions It is a tenet of Einstein's 1905 special relativity that no information can be transmitted or carried in any way at a speed faster than that of light, an idea prefigured in Maxwell's earlier theory of electromagnetic waves. When general relativity was worked out by Einstein using special relativity as a base, it was natural that it should predict that moving masses would communicate their changed gravitational fields at the speed of light, through the propagation of gravitational waves. Gravitational waves are a quintessential relativistic strong- gravitational-field phenomenon one that is completely absent in Newtonian gravitational theory. In the years since general relativity was proposed, many of its predictions have been spectacularly verified, but a few key features still remain unconfirmed. (See Section IV of this chapter.) Remarkably, one idea yet to be fully checked is the feature most closely related to the principle of relativity: gravitational waves. Just as interestingly, the eventual detection of gravitational waves will probably provide the best possible way to verify the other most spectacular of the unveri- fied predictions of general relativity: the existence of black holes. There are practical reasons that the earliest relativistic idea about gravity might be among the last to be verified. Compared to electric or magnetic forces, 32

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 33 gravity is extremely weak. This means that it is much harder to construct a practical receiver for gravitational waves than it is to construct an electromag- netic (e.g., radio) receiver. Worse, construction of a gravitational wave generator (or transmitter) from laboratory-scale components is hopeless. Einstein himself thought gravitational waves might never be detected. As is described below, new technology just coming on line is expected to be able to detect gravitational waves generated by the rapid motion of astronomical bodies whose masses are comparable to those of stars. In a radio receiver, the reception of an electromagnetic wave begins with the acceleration of electrons in the receiver's antenna by the electric field component of the electromagnetic wave. Similarly, a gravitational wave will cause motions among a set of masses that are free to move. Only relative motions are meaning- ful, though, because all objects are required to have the same free fall motion by the principle of equivalence. (For more on this principle, see Box 3.3 in Section IV of this chapter.) The measurable effect of a gravitational wave is a distortion in the distances between a set of free masses, characterized by the fractional change in distances AL/L. (It is traditional to refer to the wave amplitude h _ 2AL/L.) The strongest waves arriving regularly at Earth (say, several times per year) are expected to cause fractional length changes AL/L between pairs of detector masses separated by a distance L of no larger than about 1 part in 102~. It is this fact that scales the technological challenge of detecting gravitational waves. Still, the reception and study of gravitational waves can help answer many key ques- tions in basic physics and astrophysics: · Do waves such as those predicted by Einstein propagate away from dy- namic massive objects, and do they interact with test bodies in the way described by general relativity? . Do gravitational waves propagate at the speed of light, and do they have the polarization that general relativity predicts? · What is the nature of gravity in the strong-field regime where general relativity makes its most dramatic predictions? . Do black holes exist? What are the properties of the highly relativistic spacetime just outside their horizons? · Can we use neutron star and white dwarf binary systems to study gravita- tional physics? · Are massive black hole binaries present in galactic centers? · What is the state of matter inside neutron stars or in the collapsing cores of supernovae? · What is the origin of gamma-ray bursts? · Are there gravitational waves left over from the very early universe?

34 GRAVITATIONS PHYSICS: E~LOHNG THE STRUT OF SPACE ED TIME Achievements The Binary Pulsar and the Emission of Gravitational Waves For some years after Einstein' s initial prediction, even the existence of gravi- tational waves was in doubt, at least for some. That is no longer the case, thanks to the remarkable work of radio astronomers Joseph Taylor and Russell Hulse. In 1974, they discovered the pulsar PSR1913+16. Its frequency varied with a period of 7 3/4 hours, revealing it to be a member of a binary system. (For this reason, it was called the Binary Pulsar; now about 50 other binary pulsars are known. For background on the Binary Pulsar see Chapter 2.) Over the succeed- ing years, careful measurement of the arrival times of the pulses of radio emission from the pulsar revealed the shape of the pulsar's orbit in unprecedented detail. By recognizing a variety of relativistic effects (including orbit precession, gravi- tational redshift, and the special-relativistic time-dilation), Taylor and his co- workers were able to show that both the pulsar and its companion were neutron stars with precisely measured masses around 1.4 times the mass of the Sun. The most exciting result of these studies was the recognition that the motion of the pulsar around its companion could not be understood unless the dissipative reaction force associated with gravitational wave production was included. The two neutron stars, by virtue of their motion about one another, execute precisely the sort of motion that generates gravitational waves. Those waves carry away energy. Thus, the two stars must gradually fall closer to each other, with the result that their orbit steadily speeds up. The motion of the Binary Pulsar has shown that this orbital speedup is occurring in accordance with the rate predicted by general relativity, to a precision of a third of a percent. (See Figure 3.1.) For the discovery of this remarkable object, Hulse and Taylor were awarded the Nobel Prize in physics in 1993. Experimental Searches, Ongoing and New A gravitational wave interacts with matter by producing differential forces and thus relative motions between sets of masses. Experiments to detect gravita- tional waves involve setting up systems of a few test masses, then looking in as sensitive a way as possible for relative motions between them. Resonant detec- tors, based on the original idea pioneered by Joseph Weber in the 1960s, use a large single extended body such as a solid cylinder, whose ends may be thought of as separate masses being pulled apart or pushed together by the wave as it passes. The newer interferometric detectors use three or more small masses that are widely separated; a propagating laser beam is used to monitor their separa- tions, which will be perturbed when a gravitational wave passes.

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 35 Ll 1 1 1 1 I T 7 1 1 7 1 1 7 1 1 1 1 1 7 1 1 7 1 1 1 11 o En a) £ . _ o a) Q -5 -10 0 - 15 En al > . _ -20 -25 -30 `.. be; General Relativity Prediction' / \ / t-l I I I I I I I I I I I I I I I I I I I I I I I mu 1 975 1 980 1 985 1 990 1 995 2000 Year FIGURE 3.1 The orbital period of any body around another decreases because of the energy lost to gravitational radiation. That effect is strongest in highly relativistic sys- tems such as the binary pulsar PSR1913+16. One measure of this decrease in orbital period is the steady shift over time of the time of the pulsar's closest approach (perias- tron) to its companion star. The figure above shows the cumulative value of this shift measured by J. Taylor and J. Weisberg at the Arecibo radio telescope in Puerto Rico over several decades. The points are their data points. The solid line is the shift predicted by general relativity. The agreement is better than a third of a percent. (Courtesy of J.H. Taylor and J.M. Weisberg; to be published.)

36 GRAVITATIONS PHYSICS: E~LOHNG THE STRUT OF SPACE ED TIME Resonant Detectors. The first detector to reach astrophysically interesting sensi- tivity was the ultracold resonant bar at Stanford University, operating at 4 K (degrees above absolute zero). In 1980, it operated with a sensitivity to short bursts with strain amplitudes (AL/L) of around 1 part in 10~. The first observa- tions looking for coincident events in widely separated detectors were carried out in 1986. High-sensitivity coincidence observations were performed between an Italian detector and the Allegro detector at Louisiana State University (Figure 3.2) in 1991. This run determined the strongest upper limit yet on the flux of gravitational waves. A new generation of resonant detectors has now begun operation, using dilution refrigerators to bring their several-ton resonators to temperatures of around 50 mK (5/100 degree above zero). The pioneers of this class are the Nautilus and Auriga detectors in Italy. They should eventually attain a sensitivity of about 1 part in 102°. Designs have been produced for resonant detectors that could reach sensi- tivities of parts in 10-2~. These detectors would extend the technology already developed for aluminum cylinders to spheres as much as 10 times more massive. Interferometr~c Detectors. For many years, work on interferometers, directed at kilometer-scale devices that could achieve astrophysically motivated sensitivi- ties, was devoted mainly to proof-of-principle devices and engineering tests. Finally, in the early 1990s large interferometer construction projects were ap- proved in several countries around the world. The U.S. entry, the Laser Interfer- ometer Gravitational-Wave Observatory (LIGO), will consist of two facilities- one in Hanford, Washington, and the other in Livingston, Louisiana, each of which will contain a Michelson interferometer of arm length 4 kilometers (Figure 3.3~. (The Hanford site will also carry an interferometer of half that length for additional coincidence measurements.) When LIGO becomes operational in 2002, it is expected to be able to make unambiguous detections of waves with strains AL/L around 1 part in 102~. Similar results are expected from the 3-kilometer VIRGO interferometer (a French-Italian project located near Pisa). The British-German GEO 600-meter interferometer near Hannover has the handi- cap of shorter arm length, but early application of advanced interferometer tech- nology will allow it to be competitive in some frequency ranges, at least for a while. There is also a 300-meter interferometer called TAMA under construction near Tokyo, and an Australian project in the planning stage called ACIGA. Theoretical Studies of Gravitational Wave Sources During the last decade, the theoretical prediction of gravitational wave sources reached new levels of sophistication and promise. This effort was driven by progress in gravitational wave detectors and made possible by advances in numerical and analytic techniques for solving Einstein' s equations. The ability to

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 37 FIGURE 3.2 A view of the Allegro resonant bar gravitational wave detector at Louisiana State University. The photo shows the bar nestled in its cryogenic dewar, shortly before it was closed up. The end of the bar is visible as the circular structure in the lower half of the dewar. The rest of the internal components are structures for cooling the bar to 4.2 K, for bringing out the signal from the transducer on the bar's end, and for isolating the whole system from external disturbances. Since 1991 Allegro has functioned as the most sensitive continuously operating gravitational wave detector in the world. (Courtesy of Bill Hamilton, Louisiana State University Physics and Astronomy.)

38 GRAVITATIONS PHYSICS: E~LOHNG THE STRUCTURE OF SPACE ED TIME FIGURE 3.3 An aerial photograph of the Laser Interferometer Gravitational-Wave Ob- servatory (LIGO) facility at Hanford, Washington, in 1998. The large building in the foreground holds the vertex of the interferometers, along with the lasers, input test mass- es, and the input and output optics. The building also contains the control room, experi- ment staging areas, laboratory space, and offices for the observatory staff. One of the 4-kilometer arms disappears out of the right-hand side of the photo. The other is seen stretching to the upper left. At the 2-kilometer point can be seen a smaller building holding the end mass of the half-length interferometer that will run in parallel to the 4-kilometer interferometer, providing a local check on the observations. (Courtesy of the LIGO Laboratory.) carry out numerical simulations of gravitational collapse in three spatial dimen- sions (i.e., without restrictive symmetries), together with improvements in inte- grating realistic microphysics into the description of the collapsing stellar matter, gave results that demonstrated a remarkable sensitivity of the gravitational wave output from a supernova to the details of neutrino physics, hydrodynamics, and thermal physics. Similarly, large-scale numerical simulations of the merger and coalescence of double black hole or double neutron star systems are on the verge of achieving reliable results. (See the discussion under "Computational General Relativity" in Section II of this chapter.)

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 39 The theory of gravitational waves from the inspiral phase of double star systems was advanced using analytic tools based on the post-Newtonian tech- nique, a method for approximating solutions of Einstein's equations by succes- sive improvements on its first-order, Newtonian approximation. The results, carried to remarkably high order in successive steps, provided very accurate gravitational wave "templates," which will play a role in analysis of signals detected by LIGO-type gravitational wave detectors. The theory of small perturbations of stars and black holes, initiated in the early 1960s, was taken to new levels of development. One result was the discov- ery of entirely unsuspected unstable modes of oscillation of rotating stars, which could be promising sources of gravitational radiation and could explain the rapid spin-down of newly formed neutron stars. Another was the development of a nearly complete description of the gravitational wave emission from a small mass orbiting a massive black hole and of the "ringing" modes of distorted black holes. Finally, over the last 5 years a new method was developed to study the properties of gravitational waves emitted in the very final stages of black hole mergers. The method, called the close limit approximation, combines analytic and numerical approximation methods and has yielded fresh insights into the diverse physical processes responsible for various features of the emitted radia- tion. It paves the way for gravitational wave phenomenology along the lines of the standard quantum mechanical perturbation theory used in analyzing spectra in atomic physics. Opportunities Ground-based Reception of Gravitational Waves The decade just ending saw the National Science Foundation make a sub- stantial investment in the construction of the research facilities of the LIGO project (see Figure 3.3~. The great opportunity of the coming decade is to exploit those facilities by operating receivers of sufficient sensitivity to detect the gravi- tational waves emitted by astronomical bodies. The expectation that gravita- tional waves will be detected during the coming decade represents one of the most exciting research opportunities of gravitational physics. The spectrum of gravitational waves expected from known sources is shown in Figure 3.4. Detec- tion and study of those waves can address many of the key questions listed above. Key Questions Addressed · Do waves such as those predicted by Einstein propagate away from dy- namic massive objects, and do they interact with test bodies in the way described by general relativity?

40 GRAVITATIONS PHYSICS: E~LOHNG THE STRUT OF SPACE ED TIME 10 . E 10 1 id . _ CD 10 -22 1 0-24 "'"'' / ResolVE3d ~ Gil BlnarleS "''' ~ \ :~ . Ad-, / -4 -2 10 10 o 10 Frequency (Hz) 10 10 4 FIGURE 3.4 A schematic view of the gravitational wave spectrum, showing the project- ed sensitivity of the advanced version of LIGO and of a proposed space-based interferom- eter. LIGO and the space-based detector will each be able to look for gravitational wave sources in a band a decade or two wide. LIGO will have its best sensitivity near 100 Hz, while an instrument in space should be most sensitive near 10 mHz. The high-frequency window accessible to LIGO is best suited for studying the signals from the coalescence of neutron star (NS) binaries, and from binaries consisting of black holes (BH) with masses around 10 times that of the Sun. Binaries of massive (106 solar masses) black holes, such as are found in galactic nuclei, will be a primary target of a space-based interferometer. Each detector should also be capable of finding the signals from a variety of other astro- nomical objects, as described in the text. For example, a space-based detector would be able to record the signals of many known binary star systems. SN, supernova. (Courtesy of the Jet Propulsion Laboratory, California Institute of Technology.) The work of Taylor and his collaborators tracking the orbit of the binary pulsar PSR1913+16 established dramatically that gravitational waves were being emitted by the binary neutron star system, with a rate of energy loss in agreement with the predictions of general relativity. In a very real sense, that measurement can be said to have "detected" the emission of gravitational waves. But physicists' paradigm of establishing the existence of a wave phenom- enon is the set of l9th-century experiments on electromagnetic waves performed by Heinrich Hertz (1857-1894), which demonstrated not only energy loss in the transmitter, but also (1) propagation across spatial intervals large compared to the

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 4 wavelength and (2) excitation of test bodies in a manner consistent with the field carried by the wave. We may never have the capability to construct and manipu- late a gravitational wave transmitter, but can always rely on the existence of natural ones, as did the Hulse-Taylor binary pulsar experiment. However, receiv- ers can be built that establish that a wave propagated across the space from the transmitter and that this wave interacted with test particles in the expected way. This is the fundamental role LIGO and the other gravitational wave detectors can be expected to play, when they successfully detect the arrival of gravitational waves of astrophysical origin. · Do gravitational waves propagate at the speed of light, and do they have the polarization that general relativity predicts? The speed of gravitational waves is unambiguously predicted by general relativity to be equal to the speed of light in vacuum. Similarly, general relativity states that the polarization of the waves should be strictly quadrupolar, although other gravitation theories predict some admixture of other polarizations in addi- tion. The relativistic predictions are equivalent to the statements that the quan- tum of gravitation analogous to the photon the graviton is massless and has spin 2. (However, no detector is foreseen as being sensitive enough to detect individual gravitons.) These features of gravitational waves can be checked once the waves are detected. The polarization is most directly measured by verifying that the signal strengths detected by receivers at different locations on Earth (hence with differ- ent orientations) agree with those predicted from the source's position on the sky (as determined by time delays). The propagation speed can be checked against that of light whenever the gravitational wave emission is accompanied by some electromagnetic counterpart; examples might include the optical flash of a super- nova, or perhaps a gamma-ray burst. · What is the nature of gravity in the strong-field regime where general relativity makes its most dramatic predictions? Gravitational waves are emitted most strongly when large masses move at relativistic speeds in close proximity to one another, especially as those masses approach the degree of compactness of black holes (as in neutron stars or black holes themselves). These are inherently strong-field situations, with dynamics dramatically different than Newtonian theory would predict. The dynamics of the ultimate strong-field sources, black holes, are even more distinctive. · Do black holes exist? What are the properties of the highly relativistic spacetime just outside their horizons?

42 GRAVITATIONAL PHYSICS: EXPLORING THE STRUCTURE OF SPACE AND TIME Black holes are relativistic strong gravitational phenomena, and they show the most dramatic effects of strong gravity. The many aspects of the study of black holes are discussed in Section II of this chapter. The "cleanest" test of the existence of black holes (and of the predictions of theory regarding strong-field gravity in general) would be the measurement of the gravitational waves emitted when a black hole is disturbed, or when it forms in a gravitational collapse or merger. These waves provide a direct probe of the dynamics of the region just outside the black hole's horizon. The spectrum of the quasi-normal modes (the "ringing" of a disturbed black hole) has been exten- sively studied theoretically and should be easily recognizable in a gravitational waveform. Its most distinctive feature is that all of the modes are highly damped. The damping mechanism is the gravitational wave emission process itself. The frequency of the signal is inversely proportional to the mass; a 10-solar-mass black hole has its fundamental resonance near 1 kHz. Detection of waves from the merger phase will also probe strong-field gravity effects. Interpretation of such signals will require numerical integration of the full Einstein equations. (See "Advances in Computational General Relativity" in Section II of this chapter.) · What can we learn from the study of coalescing neutron star binaries? The gravitational wave source whose signal is most securely predicted is the coalescence of neutron star binaries, of which the Hulse-Taylor binary pulsar is a prototype. The shrinkage of the orbit of such a system is driven by gravitational radiation until the two stars coalesce, through a process that can be calculated in precise detail until nearly the final moments. The gravitational luminosity of the system grows as the orbit shrinks, with the final signal at frequencies of several hundred hertz. It is a key aim of the LIGO project to develop receivers capable of detecting several of these events per year, which means being able to detect them to dis- tances of several hundred megaparsecs (Mpc). This is the goal of the planned upgrades to the initial LIGO interferometers, scheduled to start in the middle of the coming decade. (See Chapter 1, Table 1.1, which is based on the analysis described in the addendum to this section.) When the signals from coalescing neutron star binaries are detected, we will probe strongly post-Newtonian orbital dynamics. Just as interesting will be what we will learn about the properties of nuclear matter, which will strongly influence the final phases of the orbit and ring-down of the coalesced star. It is a difficult problem to calculate the signals researchers should expect from the end of a coalescence event. This led to the formation of the NASA Neutron Star Grand Challenge effort in computational physics. (See the discussion on neutron stars under "Advances in Computational General Relativity" in Section II of this chap- ter for more details.)

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 43 · What can we learn about the state of matter inside neutron stars or in the collapsing cores of supernovae? The essential truth of the core collapse model for Type II supernovae was demonstrated only quite recently, by the detection of neutrinos from Supernova 1987A. Gravitational waves offer another way to learn about the inner workings of the collapse. The gravitational waveform is proportional to the second time derivative of the core's quadrupole moment, so it will trace the history of the collapse directly. The gravitational waveform will emerge without any absorp- tion by the outer layers of the star, unlike all other signals (including neutrinos). The strength of the signal (and thus the rate of detectable signals) depends on the degree to which the core is in fact endowed with a quadrupole moment. Recent calculations have begun to suggest the possibility of non-negligible departures from spherical symmetry, although the amplitudes predicted still would not make this a very strong signal. Whether the strong kicks that newborn pulsars appear to receive could be related to an asymmetric collapse is also uncertain. . What is the origin of gamma-ray bursts? Some of the most popular models for gamma-ray bursts involve the collision of two neutron stars. If these ideas are correct, then for some bursts there should be coincident gamma-ray and gravitational wave signals, presumably with a gravitational wave precursor from the inspiraling stars. Other popular models of gamma-ray bursts involve collisions of black holes or core collapse events inside massive stars; either of these classes of models also would generate coincident gravitational wave signals. Whether or not such models turn out to be correct, gravitational wave observations will make an important contribution to the un- derstanding of the enigmatic gamma-ray bursts. . Are there gravitational waves left over from the very early universe? A gravitational wave background from the early universe, if it is detectable, would provide the earliest possible glimpse of the history of our universe. It is hard to predict the strength or the frequency of such signals and also hard to distinguish such signals from other sources of noise. Nevertheless, LIGO will search for this effect, as will a space-based detector. The issues are described in more detail below in "Space-based Reception of Gravitational Waves," in the discussion of key questions addressed by space-based detectors. LIGO Operation and Sensitivity Enhancement. The LIGO initial data run (2002- 2003) will represent a genuine milestone: its sensitivity of 10-2i will be nearly 3 orders of magnitude in amplitude (6 orders of magnitude in energy) more

44 GRAVITATIONS PHYSICS: E~LOHNG THE STRUT OF SPACE ^D TIME sensitive than the best previous searches. Discovery of gravitational wave sig- nals at this sensitivity could occur. But the search for gravitational waves has to be viewed as a long-term effort. This is not because there is uncertainty about whether gravitational waves exist or about their theoretical underpinning. Gravitational waves have been detected indirectly through the analysis of the orbit of the Hulse-Taylor binary pulsar, in excellent agreement with the predictions of general relativity. Rather, there is uncertainty concerning the frequency of violent events in the universe which could produce gravitational radiation strong enough to be detected on Earth. Uncertainty in the abundance of sources means that no precise sensitivity thresh- old for the first detection can be specified. The only sensible strategy for success is to press ahead with two activities simultaneously: aggressive development of the technology for more sensitive interferometers, and the installation and opera- tion of advanced interferometers as they become available. It may be that the only sources of gravitational waves are the ones we already know about from previous (electromagnetic) observations. If in fact the universe holds so few surprises, then LIGO will first detect the signals from coalescing neutron star binaries. The COP's estimates for the event rate for these is dis- cussed in detail in the addendum to this section. Given these estimates, an improvement in sensitivity of around a factor of 10 from that characterizing the initial data run will probably be required to detect these signals regularly. An R&D program aimed at achieving the indicated sensitivity enhancement has started. Designs are now laid out that would improve LIGO's sensitivity by around a factor of 10. Development of key technologies is under way. As shown in Table 1.1 in Chapter 1, LIGO's plans call for the implementation of these enhanced-sensitivity interferometers around the middle of the next decade. Plans for even more sensitive interferometers have also begun to be formu- lated. This line of research is critical; its results may be required to guarantee the detection of gravitational wave signals, if the most pessimistic estimates of event rates are correct. Even in the happy event that signals are detected sooner, improvement in signal-to-noise ratio and in event rate will pay big dividends in the scientific value of gravitational wave observations. Space-based Reception of Gravitational Waves Key Questions Addressed. While LIGO's promise is great, its observations will necessarily be limited by terrestrial noise sources to a frequency band above about 10 Hz. A space-based interferometer can open the frequency band between roughly 10= Hz and almost 1 Hz. Completely different classes of gravitational wave sources will be observable at these lower frequencies. Several key technologies necessary to implement such a gravitational wave detector still need development. Nevertheless, the promise of a space-based detector is enormous. At the sensitivity that can reasonably be expected, there

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 45 are numerous sources of gravitational waves that will be detected with signal-to- noise ratios of hundreds to thousands. The COP discusses below four scientific opportunities that an appropriately designed space-based gravitational wave de- tector should allow us to achieve. · Can we use white dwarf binaries to study gravitational physics? The low-frequency gravitational wave band contains the signals from white dwarf binaries. These have the tremendous advantages that both their waveforms and their strengths can be confidently predicted. Their quadrupole moments can be calculated in a straightforward way, and their distances are well known from many years of astronomical study. Those signals ought to be relatively easily detected by the sorts of space-based detectors now being proposed. Thus, the cleanest possible tests of gravitational wave theory can be made by observing the waves emitted by a source of precisely known properties. Detectable signals will be numerous, so much so that, at the lowest frequencies, their periodic signals will overlap in a "confusion limit" that will constitute one of the chief noise sources. . Are massive black hole binaries present in galactic centers? The frequency band accessible from space contains the signals from black holes in the 103 to 106 solar mass range. The upper end of this mass range is characteristic of the black holes known to populate many galactic nuclei. Mas- sive black hole binaries could result from the merger of two galaxies, each con- taining a single massive black hole. The role these black holes play in galactic activity, and the importance of galactic mergers, are two of the key questions of extragalactic astronomy. (For more on this, see "Supermassive Black Hole Merg- ers and Space-based Detectors" in the addendum to this section.) If a binary of two such black holes were to coalesce anywhere within the visible universe, the resulting gravitational wave signal should be detectable at very high signal-to- noise ratio by the planned space-based interferometers. . What are the properties of the highly relativistic spacetime just outside black hole horizons? One of the key ideas of the theory of black holes is that they are each entirely describable by three numbers: mass, spin, and charge. (In astrophysical situa- tions, the charge is expected to be extremely small.) This is called the "no hair" theorem since it accords black holes so little individuality. These three numbers completely determine the nature of a black hole's spacetime. A space-based interferometer could measure the waves from black hole binary coalescences in such detail that any departure from the predictions of the "no hair" theorem can be sensitively tested.

46 GRAVITATIONS PHYSICS: E~LOHNG THE STRUT OF SPACE ED TIME . Are there gravitational waves left over from the very early universe? Just as our ability to probe the interior of a supernova electromagnetically is frustrated by the opacity of the outer layers of the star, so too do our electromag- netic probes of the universe run into the opaque "surface of last scattering," when hydrogen was last ionized about 300,000 years after the big bang. Gravitational waves emitted before this epoch could be bathing Earth. The simple gravitational analog of the electromagnetic cosmic background radiation would be too weak to be detected. But some processes that might have occurred during inflation, or others associated with cosmic phase transitions, could lead to detectable levels of gravitational waves. Distinguishing such a background of waves from other sources of noise will be challenging. Still, no other astronomical tool even holds out the hope of enabling a look at the Planck-scale physics of quantum gravity. Thus gravitational wave observations could play a key role in supplying evidence for a theory of quantum gravity. (See the discussion of ideas about quantum gravity in Section V of this chapter.) R&D Toward a Space-based Gravitational Wave Detector. Planning is under way for detectors able to explore the low-frequency window, which is accessible only from space. To make the detectors a reality, it will be necessary to carry out a program of technology development to ensure that the required performance specifications can be reached. Development of inertial sensors, drag-free attitude control, very long baseline optical interferometry, and ultrastable mechanical structures is required. When these technological developments have been achieved, then the scientific case for deploying a space-based gravitational wave detector will be overwhelmingly strong. Related Opportunities Gravitational Wave Theory. The effort to study and detect gravitational waves requires not only the effort of scores of experimental physicists and engineers, but also the help of many theoretical physicists as well. A multifaceted program of research in gravitational wave theory is necessary to ensure that signals can be efficiently extracted from LIGO's data stream, and be used to address the key questions. Some theorists will design the software that will enable the large quantities of data to be efficiently archived, while others are helping to develop the algo- rithms for optimally extracting signals from the detectors' data streams. Others will continue to work to understand as well as possible the predictions of the theory of general relativity, so that we will be ready to recognize the signals created by the astronomical sources of gravitational waves. Some of this theo- retical work has been of the traditional analytic style. Another part of this pro- gram involves the numerical solution of the Einstein equation; this is probably

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 47 the only way to deal with the highly relativistic final stages of binary coalescence, for example. Still other parts of the theoretical effort have the flavor of astro- physics, trying to predict the abundance of objects that will serve as strong gravitational wave sources. The Connection Between Gravitational Waves and Other Astronomical Obser- vations. In a nascent branch of astronomy like gravitational wave detection, success will be greatly aided by making the strongest possible link to other branches of astronomy. For example, new observations from the Compton Gamma Ray Observatory (CGRO) satellite (and more recently from BeppoSAX) have sparked a strong suspicion that the enigmatic gamma-ray bursts may result from the merger of two neutron stars. Since that is precisely the kind of event expected to give detectable gravitational wave signals, there exists the possibility that gravitational wave observations can help to resolve one of the outstanding puzzles in astronomy. By the same token, ongoing observations of gamma-ray bursts may allow a more sensitive search for the gravitational wave signals, by establishing the arrival times of the signals at Earth. Another kind of violent astrophysical event that may create strong gravita- tional waves is the stellar core collapse that initiates a Type II supernova. As in the case of gamma-ray bursts, knowledge of the times of nearby supernova events will help both in possible gravitational wave signal detections and in testing models for the strength of the emitted waves. Neutrino observations from current and planned detectors may provide an observation of core collapse from a nearby supernova. Coincident detection of a gravitational wave signal would yield new insights into the nature of the collapse. In these and other possible cases, it is expected that gravitational wave detec- tion and electromagnetic astronomy will complement each other in the study of some of the most dramatic events in the universe. For this scientific cross- fertilization to lead to the richest possible results, it is important to support astro- nomical research likely to overlap with gravitational wave observations. Astro- nomical study of compact objects, especially the carrying out of all-sky surveys for transient events in the optical, x-ray, and gamma-ray bands, will continue to play an important part in gravitational wave research. Searches for Gravitational Waves of Cosmological Origin. Although our under- standing of the physics of the universe in its very early stages is still primitive, we do know that if the universe began violently, then gravitational waves arriving today will carry the imprints of those first few moments. If a phase transition after the first moments produced a background of gravitational waves, then inter- ferometric observation (possibly ground-based but more likely space-based) is one means to search for it, as discussed in the sections on ground-based and space-based observations above. Pulsar timing experiments, which examine longer wavelengths, are also sensitive probes.

48 GRAVITATIONAL PHYSICS: EXPLORING THE STRUCTURE OF SPACE AND TIME On the other hand, if a background of gravitational waves was produced by cosmological inflation, then it could have a spectrum that makes the study of the cosmic microwave background's polarization the most sensitive probe. In the absence of a clear understanding of the early universe, it is reasonable to pursue the search for these relics of the earliest instants of our history on as diverse a spectrum of wavelengths as possible. Even upper limits in any range of wavelengths can provide important information on early universe physics. For example, if the radiation is less than predicted from the merger of bubbles arising in first-order phase transitions or from the evaporation of cosmic strings, that would yield a much clearer picture of the nature of inflation and the origin of fluctuations.

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 49

50 GRAVITATIONAL PHYSICS: EXPLORING THE STRUCTURE OF SPACE AND TIME

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 5

52 GRAVITATIONAL PHYSICS: EXPLORING THE STRUCTURE OF SPACE AND TIME Key Questions Perhaps no other object from physics has had as much impact on public consciousness in recent times as the black hole has. General relativity predicts that black holes will be formed whenever sufficient mass is compressed into a small enough volume. The gravitational force at the surface becomes so large that nothing can escape, no matter how fast it accelerates. Not even a beam of light can escape, hence the name black hole. Black holes are quintessential strong-gravity phenomena. It is not possible to compress matter on Earth enough to make a black hole. But on astronomical scales, gravity itself can do the job. When a very massive star reaches the endpoint of its thermonuclear burning phase, nuclear reactions no longer supply thermal pressure, and gravitational collapse can proceed all the way to a black hole. By contrast, the collapse of a somewhat less massive star halts at high density when the core is transformed entirely into nuclear matter. The envelope of the star is blown off in a gigantic supernova explosion, leaving the core behind as a nascent neutron star. Gravitational collapse of very massive stars is expected to produce black holes with masses of a few or a few tens of solar masses. Several candidate black holes have been discovered. In addition,

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 53 there is evidence for supermassive black holes, with masses ranging from a million to a few billion solar masses, in the centers of galaxies. These large black holes may be produced by the gravitational collapse of a supermassive gas cloud or via the growth of a seed black hole that captures stars and gas from a dense star cluster. Three key questions confront us about black holes: · Do black holes actually exist in nature? Are the black hole candidates of astrophysics the black holes of general relativity? · What are the detailed properties of black holes as predicted by Einstein's theory? . If black holes do exist, what observations can we carry out to confirm that they have the properties predicted by general relativity? The discovery of real examples of black holes has been a central goal of gravitational physics for many years. Several excellent black hole candidates have been identified by astrophysicists, and we speak loosely of black holes having been discovered. What has actually been discovered are objects with a large amount of mass in a small region. By a process of elimination, we conclude that they must be black holes. But so far there is no convincing evidence that any of the candidates has the distinguishing features of a black hole, such as an event horizon, the one-way membrane that prevents anything from escaping. A black hole is the most compact configuration of matter possible for a given mass; for a mass M, the size of a black hole is given by the Schwarzschild radius, Rs = 2GM/c2. One way of verifying the compactness of a candidate black hole is by measuring the speed of matter in orbit around it; the speed is expected to approach c in the vicinity of the horizon. This test is feasible since orbiting gas flows, called accretion flows, are common around gravitating objects in the uni verse. In a few objects, direct evidence for high orbital speeds is obtained by mea- suring the Doppler broadening of spectral lines from the accreting gas. In addi- tion, many black hole candidates exhibit gas outflows, or jets, with relativistic speeds. Such motions require an object with a relativistic potential, hence sug- gesting a black hole. A more indirect indication of compactness comes from observations of strong x-ray emission from the accreting gas. The radiation requires temperatures in excess of 109 K, which is most easily achieved with a relativistic object. When the radiation (typically x-rays) from a compact object varies on a characteristic time scale t, the size of the object must be less than the distance light can travel in this time, ct. If the size limit thus computed is comparable to Rs, the object can be identified as a candidate black hole. For solar-mass black holes, this implies looking for variability on a time scale less than a millisecond, whereas for supermassive black holes the relevant time scale is minutes to hours.

54 GRAVITATIONS PHYSICS: E~LOHNG THE STRUT OF SPACE^D TIME Unfortunately, the demonstration of compactness alone is not sufficient to identify a black hole; a neutron star, with a radius of about 3 times Rs, is only slightly larger than a black hole of the same mass. Neutron stars can exist happily in equilibrium for small enough masses. But beyond a certain critical mass, the inward pull of gravity overwhelms the balanc- ing pressure force and the star will collapse to a black hole. This then provides one of the key astronomical signatures of a black hole: Look for a system containing a dark massive object. If the object is compact enough and if its mass is greater than the maximum allowed mass of a neutron star, then we infer that it must be a black hole. The value of the maximum neutron star mass is uncertain theoretically be- cause we do not understand nuclear physics well enough to calculate it reliably. Current conventional nuclear equations of state predict a maximum mass around 2 solar masses, but our confidence in this value is not high. Because of this uncertainty, astrophysicists generally rely on a calculation that assumes we un- derstand nuclear physics up to some density, and then varies the pressure-density relation over all possibilities beyond this point to maximize the resulting mass. This procedure yields an upper limit to the maximum mass of around 3.2 solar masses. Rotation increases the amount of matter that can be supported against collapse, but only by about 25 percent even for stars rotating near breakup speed. Circumventing these limits would require us to accept some unconventional phys- ics much more unconventional than black holes! Thus, any compact relativistic object with a mass above about 3 solar masses is considered an excellent black hole candidate. By this criterion, a number of very good black hole candidates have been discovered in the nuclei of galaxies, including our own, and in x-ray binaries. However, the evidence that these candidates are black holes is still somewhat indirect, since what can be demon- strated is only that the objects are not neutron stars. Direct proof that a candidate is a black hole requires a demonstration that the object has an event horizon, the one feature that is unique to a black hole. Such proof does not currently exist for any astronomical object (but see Box 3.1 on energy advection). The detection of gravitational waves from the final merger of a pair of black holes in a binary will probably provide even firmer proof. Finding absolutely incontrovertible evidence for a black hole in nature would be the capstone of one of the most remarkable discoveries in the history of science. Achievements Astrophysical Black Hole Candidates Black hole candidates have been discovered in x-ray binaries distributed throughout our Galaxy. Each of these x-ray-emitting double stars consists of a compact star that strips gas gravitationally from the outer layers of its more

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 55 normal companion. The x-rays are produced when the stepped gas swirls down to the compact star through an accretion flow. Spectroscopic observations, coupled with a simple application of Newton's laws of mechanics and gravity, allow astrophysicists to set a firm lower limit on the mass of the x-ray-em~tting star. In half a dozen x-ray binanes, the lower limit on the mass thus obtained is greater than the maximum mass of a neutron star. These objects are among the best black hole candidates in astrophysics. Several x-ray binaries exhibit rapid variability in their x-ray emission, including very interesting quasi-penodic oscillations that are yet to be understood, and a few exhibit relativistic jets. These observations confirm that the objects are very compact. The discovery in the 1960s of luminous quasars prompted astrophysicists to consider the possibility that supermassive black holes may have existed at the centers of galaxies when the universe was young. It appeared likely that present- day galaxies would contain dead quasars as massive black holes in their nuclei. Evidence for these black holes has accumulated rapidly in recent years. The new evidence has emerged primarily from improved observational capa- bilities in the optical, infrared, and radio bands, both on Earth and in space. Detailed spectroscopic studies of the central regions of galaxies allow us to measure the gravitational effect of a candidate black hole on the line-of-sight velocities of gas and stars. These measurements show that most nearby galaxies contain dark supermassive objects with masses in the range from 106 to 10~° solar masses. The nuclei of our own Milky Way Galaxy and the galaxy NGC 4258 (see Figure 3.5) have been studied particularly well since astronomers are able to FIGURE 3.5 pages 56 and 57 Evidence for the presence of a supermassive black hole in the galaxy NGC 4258. The top panel is an artist's sketch of the molecular accretion disk at the center of this galaxy which was detected by means of its water vapor maser emission. Below this is the spectrum of the emission. The middle picture shows a radio image of the very center of the disk. The small clumps are the images of the maser- emitting water clouds obtained with radio interferometry superposed on a grid represent- ing the unseen portions of the disk. The plot in the lower left shows the line-of-sight velocities of the clouds as a function of position along the major axis of the image. The velocities trace a Keplerian profile, corresponding to a central mass of 3.5 x 107 solar masses. The deviations from Keplerian behavior are so small (less than 0.3 percent) that we can be sure the central mass lies almost entirely inside the inner edge of the disk at 0.13 parsec. The mass density of the object is thus extremely large, greater than 4 x 109 solar masses/parsec3. Given the large mass and high density, it is hard to imagine the object being anything other than a black hole. The image in the lower right panel shows radio emission from the jets that emerge along the spin axis of the molecular accretion disk (the jets are indicated by the blue cones in the artist's sketch). (Courtesy of James Moran and Lincoln Greenhill, Harvard-Smithsonian Center for Astrophysics.)

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58 G~V~ATION~ PHYSICS: E~LOHNG THE STRUT OF SPACE ED TIME BOX 3.1 Energy Advection and the Black Hole Event Horizon Gas accreting onto a compact object such as a black hole invariably has angu- lar momentum and first goes into orbit around the object. Friction in the disk of accreting gas slows its rotation, allowing the gas to spiral into the center. The viscous forces also produce heat, just as ordinary friction both slows down a mov- ing object and generates heat. In the case of accretion onto a black hole or a neutron star, the amount of heat released is very large, about 102° ergs for every gram accreted. In a thin accretion disk, the gas promptly radiates away the heat released by viscosity. In contrast, in an advection-dominated accretion flow (ADAF), only a small fraction of the heat energy is radiated; the bulk of the energy is transported, or "advected," to the center. What happens to the energy in an ADAF when it reaches the center? If the central object is a black hole, the energy simply disappears through the event horizon, never to be seen again. On the other hand, if the object has a surface, the energy will be re-radiated; this radiation will dominate the observed radiation from the system and will have a recognizable signature in its spectrum. It is thus possi- ble, in principle, to distinguish black holes from objects with surfaces. So far, the evidence is that several candidate black holes do have event hori- zons. This is the most direct indication yet that black holes are present in nature. The evidence is, however, not conclusive. ADAF models assume without proof a two-temperature gas, where protons and other atomic nuclei are much hotter than electrons. A larger uncertainty has to do with outflows. The evidence for the event horizon is principally one of missing energy. But if the gas were simply to flow out of the system and not accrete, there would be no missing energy. These complex issues need more study. measure both the line-of-sight velocities and transverse velocities of stars and gas. The center of the Milky Way is close, and the galaxy NGC 4258 has strong maser emission with which the velocity of the matter in its central regions can be mapped with precision. The results of these studies are that the center of our Galaxy has a dark object of a few times 106 solar masses, and NGC 4258 has an object of a few times 107 solar masses. The dark objects in these and other galactic nuclei are much too massive to be neutron stars. Furthermore, several of them emit x-rays and many have jets. For these reasons, they are considered strong black hole candidates. While there is no doubt that both these classes of objects described above are compact enough to be black holes and are too massive to be neutron stars, scien- tists cannot yet claim victory. The black hole is one of the most extraordinary objects in all of physics. We cannot accept its reality merely by showing that a candidate object is not a neutron star. More compelling proof is required. Ide- ally, we would like to see direct evidence that the object has an event horizon. Failing this, we would at least like to see strong evidence that space in the vicinity

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 59 of the object is curved in the manner described by Einstein's theory. Some progress has been made on both fronts via astrophysical observations and model- ing. Most of the information we receive about black hole candidates is through radiation emitted by accreting gas. Substantial theoretical effort has gone into understanding the physics of accretion flows and modeling the observations. Two kinds of accretion are now recognized to be important. One form, called an advection-dominated accretion flow, has provided a tantalizing hint that some black hole candidates may actually possess event horizons as predicted by gen- eral relativity (see Box 3.1~. The second form of accretion, called a thin accretion disk, has also proved useful. From Doppler studies of fluorescent iron emission in x-rays, we have preliminary evidence for spacetime curvature near black hole candidates. These studies, which are still in their infancy, are very promising as a probe of the environment around black holes. Spectral models of thin disks in x-ray binaries have also allowed us to estimate the rate of spin of a few black hole candidates. Finally, models of the oscillation modes of thin disks are being compared to observed variability in x-ray binaries. Such studies may provide powerful diagnostics of relativistic effects in the vicinity of black hole candi- dates. Advances in Computational General Relativity Black Holes. While many remarkable properties of black holes have been un- covered by analytic techniques, the astrophysically significant problems of black hole formation and black hole collisions require numerical solution of Einstein's equations. Such simulations can also yield an understanding of other features of Einstein's theory (see the section "Insights into the Structure of Spacetime" below). Already in the 1960s there were attempts to numerically simulate gravi- tational collapse to black holes and the head-on collision of two black holes. Progress was slow at first, in part because of inadequate computer power but also due to difficulties in understanding many technical issues. The past decade, by contrast, has seen a flowering of computational general relativity. The next decade could see a transformation of gravitational physics as large-scale comput- ing allows the treatment of ever more complicated spacetimes. A major undertaking of the 1990s was the Binary Black Hole Alliance sup- ported by the National Science Foundation as a Grand Challenge effort in compu- tational science. The alliance was a multi-institution collaboration of computa- tional physicists and computer scientists developing and applying the cutting-edge computational infrastructure necessary to tackle simulations of black hole colli- sions. The alliance focused on the calculation of the coalescence of two black holes in binary orbit as the system loses energy by gravitational wave emission. This is the simplest problem that includes the full panoply of general relativistic difficulties gravitational waves, black holes and their associated singularities, and dynamics in three spatial dimensions with no symmetry. It also happens to

60 GRAVITATIONAL PHYSICS: E~LOHNG THE STRUCTURE OF SPACE AND TIME be a very important problem for gravitational wave detection (see Section I of this chapter). Moreover, developing the ability to solve this problem would provide a basis for solving other astrophysically interesting problems involving Einstein's equations. Among the accomplishments of the Binary Black Hole Alliance were the following: (1) development of the "apparent horizon boundary condition" tech- nique to excise a black hole from the computational domain, thereby avoiding the singularity inside; (2) development of new "hyperbolic" formulations of Einstein's field equations; these new formulations have better mathematical prop- erties than the standard formulation and are likely to lead to more accurate simu- lations; (3) a highly successful collaboration with computer scientists, culminat- ing in the production of the Distributed Adaptive Grid Hierarchy (DAGH), a software package that supports the solution on large parallel supercomputers of the equations encountered in numerical simulations of general relativity; and (4) detailed results of black hole physics, such as the geometry of the black hole surface as black holes merge (see Figure 3.6~. The Binary Black Hole Alliance has taken computational general relativity from simulations in two spatial dimensions to full three-dimensional simulations, and its results suggest that the ultimate goal of simulating something as compli- cated as two black holes in binary orbit is within reach. Neutron Stars. The astrophysics of stellar-mass black holes is inextricably bound up with that of neutron stars, whose coalescence to form a black hole may pro- vide an important source of detectable gravitational radiation. The methods of computational general relativity can play a significant role in several important astrophysical problems involving neutron stars. On the one hand models of binary neutron stars are simpler to construct because they do not have to handle event horizons and singularities, but on the other hand they must deal with the complications of neutron star matter. The NASA Neutron Star Grand Challenge effort to model coalescing binary neutron stars was recently concluded, in part building on the techniques developed by the Binary Black Hole Alliance. The binary neutron star problem is, among other things, of great interest for gravitational wave detectors such as LIGO (see Sec- tion I of this chapter). The structure and stability of rapidly rotating neutron stars represent an astrophysical problem of great importance. Millisecond pulsars spin fast enough that rotational effects are important in their structure, and there is great potential for learning about properties of nuclear matter from observations of rapidly rotat- ing pulsars. During the past decade fully relativistic simulations of spinning neutron stars have become possible with arbitrary nuclear equations of state. There has also been a significant breakthrough in understanding the stability of these models. Even in Newtonian gravity, diagnosing the stability of a rapidly

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 6 FIGURE 3.6 Head-on collision of two black holes to form a single black hole that becomes spherical at late times. The location of the black hole horizons in the numerically generated spacetime is found by tracing the path of light rays (yellow) that just fail to escape to infinity. Time t is plotted on the vertical axis, z is the symmetry axis, and p is the other cylindrical coordinate axis. The coordinate angle o is suppressed in the figure. (Courtesy of Joe Libson, Joan Masso, Edward Seidel, Wai-Mo Suen, and Paul Walker, National Center for Supercomputing Applications, University of Illinois at Urbana-Cham- paign.) rotating star against nonaxisymmetric perturbations is a difficult problem. It was reduced to a tractable form only in 1989. The analogous reduction in general relativity was accomplished in 1996 and is even more complicated. Neverthe- less, reliable statements about stability can now begin to be made for the first time.

62 GRAVITATIONA:L PHYSICS: EXPLORING THE STRUCTURE OF SPACE AND TIME Black Hole Entropy The past decade has continued to see exciting progress in our theoretical understanding of the properties of black holes. It has been known since the early 1970s that black holes satisfy several rules that are very similar to the familiar laws of thermodynamics. In particular, black holes have an analog of the usual temperature and entropy. Over the last 5 years, these thermodynamic considerations were extended from general relativity to a large class of relativistic theories of gravitation. In the early 1970s, it was believed that these similarities were only math- ematical. How could the black hole have a physical temperature since a hot object emits radiation while a black hole is an object from which nothing can escape? This view changed completely with the discovery of Hawking radiation, which demonstrated that, because of quantum effects, black holes do radiate like a hot object. In all contexts in physics, thermodynamic behavior is the result of averaging over a large number of different microscopic configurations with the same mac- roscopic properties. In particular, the entropy is related to the number of micro- states with the same macroscopic parameters. For a black hole, the entropy turns out to be proportional to its area in units of the Planck length squared 10-66 cm2. This is an enormous number, much larger than the entropy of a corresponding amount of ordinary matter. Physicists have tried for more than 20 years to understand the origin of this enormous entropy. Recently, an explanation has been found in quantum gravity. Quantum states of some black holes can be counted, and the result is in complete agreement with the thermodynamic predic- tion. Some aspects of Hawking radiation have also been reproduced starting with the microscopic theory. See Section V of this chapter for further discussion. Insights into the Structure of Spacetime One of the great open questions in general relativity is the outcome of the gravitational collapse of a general configuration of matter. Powerful theorems require the formation of a singularity from well-behaved initial conditions, if the gravitational field becomes strong enough to trap light. At a singularity, the predictive capabilities of general relativity break down. Indeed, the occurrence of singularities is one of the motivations for the search for a quantum theory of gravity, in which such behavior would not happen. In the simplest, best-known, and analytically calculable example the spheri- cally symmetric collapse of a pressureless fluid the eventual singularity is hid- den deep within the event horizon of the black hole that is formed. Information from the singularity inside the black hole cannot reach any observer outside the event horizon, so physics can proceed normally outside. What happens in spacetimes without the special symmetries of this example? What happens with more realistic models of the collapsing matter?

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 63 An astrophysically interesting possibility is a "naked" singularity a region of infinite tidal force and breakdown of physical laws that is visible (thus "na- ked") to observers far away from it. Even though quantum effects can be ex- pected to prevent true infinities from actually occurring, the possibility of naked singularities is an issue that must be resolved within classical (not quantum) gravitation to see when the classical theory breaks down. The idea that naked singularities are never formed from realistic initial conditions is known as the cosmic censorship conjecture. An important development during the past decade has been a synthesis of analytic and numerical techniques to investigate the validity of the cosmic cen- sorship conjecture. Proofs of cosmic censorship were found in certain simplified (but not trivial) cases that assume special symmetries. It was also shown, using sophisticated analytic methods, that an initial state of weak but otherwise arbi- trary nonlinear gravitational waves does not develop singularities. The waves disperse, leaving flat spacetime. Numerical studies of highly nonlinear gravitational collapse of a matter field showed that naked singularities could form if the initial amplitude of the field is exactly right. If the amplitude is larger a black hole forms. To study the transi- tion between the weak- and strong-field results, sophisticated numerical simula- tions were required. This program led to the 1993 discovery that black hole formation is accompanied by critical behavior, analogous to the critical behavior seen in many physical systems at a phase transition. (In this case, the "transition" is between not forming a black hole and forming a black hole.) Subsequent work has focused on analyzing the generality of this critical behavior in Einstein's equation. This is an example of how the combination of analytic methods and numerical simulation can uncover new fundamental qualitative features of the theory. Opportunities Detection and Study of Gravitational Waves from Merging Black Holes The discovery of signals from the merger of a binary black hole system, and the demonstration that the signals are indeed from black holes, would be a spec- tacular achievement. All the astrophysical probes described elsewhere in this section provide only indirect information on physics near the event horizon. Gravitational waves from a binary merger, on the other hand, come directly from the sloshing event horizon of the merged object. This is the most direct probe we are likely to have of the very essence of a black hole its event horizon. The building of gravitational wave detectors sensitive to such signals is, therefore, of the utmost importance for the field (see Section I of this chapter). Confronting theoretical predictions with the observationally determined properties of black holes would provide a scientific bonanza.

64 GRAVITATIONA:L PHYSICS: EXPLORING THE STRUCTURE OF SPACE AND TIME Binary black hole-black hole and black hole-neutron star systems, with black hole masses of around 10 solar masses, are very likely to form as a natural consequence of stellar evolution. Some of these systems are expected to merge (as a result of the loss of energy and angular momentum in gravitational waves) within a time less than the age of the universe. The mergers of such binaries in moderately distant galaxies could be detected with gravitational wave receivers such as LIGO. Theoretical predictions of the event rates are uncertain, but it is possible that these might be the first signals that LIGO sees. (See "Binary Neutron Star Mergers and LIGO" in the addendum to Section I of this chapter.) Binary supermassive black holes, with masses of 106 to 10~° solar masses, are very likely to form and merge in the centers of many galaxies (see "Supermassive Black Hole Mergers and Space-based Detectors" in the adden- dum to Section I of this chapter). Such mergers occur naturally in the current paradigm of hierarchical galaxy formation. Mergers of supermassive black holes in even the most distant galaxies in the universe could be easily detected with space-based interferometers. This is one of the strongest reasons for building such detectors. Computational General Relativity Computer simulations of Einstein's equations are necessary to calculate the detailed shape (the waveform) of the gravitational waves emitted by the inspiral and merger of binary black holes or neutron stars in the strong-field regime. Such waveforms can be used to improve the chances of detecting signals with LIGO and space-based detectors. In addition, a comparison between the predicted waveforms and those observed is likely to provide the best evidence that black holes have the properties that Einstein's theory predicts. The Binary Black Hole Alliance moved computational general relativity into fully three-dimensional problems, and the Neutron Star Grand Challenge col- laboration built upon that foundation. They proved the value of multi-institution collaborative efforts on problems too large to be solved with the efforts of a single investigator. To realize the opportunity that has thereby been created will require careful attention from funding agencies so that the expertise that has been assembled does not dissipate. In addition to the human resources, significant access to computing resources will be required. To calculate the waveform from the last orbit and coalescence of a binary black hole system with a modest accuracy of around 10 percent, researchers would need computer runs taking 12 hours on a machine running at 10 teraflops and requiring more than 10 terabytes of memory. Fully three- dimensional black hole calculations will continue to push the envelope of what is possible on the largest machines in the coming decade. Pulsar searches in the coming decade are likely to become sensitive to peri- ods of 1 ms and less. If nature provides us with such rapidly spinning pulsars,

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 65 there is great potential for learning new aspects of nuclear matter at high densi- ties. This will require further development of codes to study the stability of rapidly rotating neutron stars. In astrophysics, general relativity is routinely invoked to explain observa- tions but is seldom used in calculations because it is too complicated. This will change as algorithms from "pure" general relativity codes are used in conjunction with the microphysics of astrophysics codes. Prime examples involve nonspheri- cal supernova calculations and simulations of neutron star mergers, but it can also be expected that the modeling of phenomena involving quasars, x-ray binaries, and gamma-ray bursts will begin to incorporate general relativity. Detection and Study of Black Holes by Astrophysical Means As described in the previous parts of this section, astrophysicists have dem- onstrated beyond reasonable doubt that there exist objects in the universe that are extremely compact and that cannot be neutron stars. The key goal now is to show that these objects are genuine black holes as understood within general relativity. We must show that the objects warp spacetime in their vicinity in the manner predicted by Einstein's theory. We must show that the objects have that most remarkable of features the event horizon. To do this, we need to study regions close to the black hole. Radiation from gas accreting onto a compact object provides many clues about this critical region. It is in the observation and modeling of the radiation, especially in the x-ray band, that the best opportunities are likely to be found. The spectral shape of x-ray line profiles from orbiting gas flows can be used to measure the warped geometry in the vicinity of a black hole. The study of fluorescent emission from iron atoms, for instance, has already provided prelimi- nary information on the properties of spacetime near a black hole. The expanded capabilities of future x-ray missions should enable researchers to use this and related probes with much greater precision. We should be able to measure the rate of spin of black holes or even detect the dragging of inertial frames by a spinning hole. Time variability studies of the x-ray emission may also have large payoffs. Noise spectra and the discovery of quasi-periodic oscillations have already led to new insights on accreting neutron stars. The extension of these studies to black holes is clearly the next frontier in this rapidly growing field. While the above studies will enable us to examine the environment near a black hole, investigations of advection-dominated flows (see Box 3.1) may lead to confirmation of the event horizon itself. To achieve this goal, observations must be done over a wide range of the electromagnetic spectrum, from radio to gamma-rays. The observations are difficult since the systems are very dim, but they are worthwhile, especially if theoretical models can be improved. In par- ticular, it is important to investigate whether the signatures that have been associ

66 GRAVITATIONA:L PHYSICS: EXPLORING THE STRUCTURE OF SPACE AND TIME ated with the presence of an event horizon could be attributed to other effects such as mass outflows. These studies will of necessity concern a few chosen systems. It is impor- tant, however, that we continue to search for more black hole candidates, both in the nuclei of galaxies and in x-ray binaries. Each new system that we discover is in some sense unique. Somewhere out there, doubtless, is a system that could become the "Rosetta stone" of black hole astrophysics. The only way we will find it is by continuing to search with the best telescopes that can be built on Earth and in space. Increasing the population of known black hole systems will also lead to a better understanding of many statistical questions. In particular, the question of event rates for gravitational wave detectors requires more observa- tional input for better estimates. All this requires that we update and maintain the infrastructure for astro- nomical observations. X-ray and gamma-ray observatories in space, high-resolu- tion optical and infrared telescopes on Earth and in space, and radio interferom- eters are all important. Adequate support should also be provided for theoretical work and interpretive modeling. Analytical Studies of the Structure of Spacetime Substantial further progress on elucidating compact binary inspirals and col- lisions, cosmic censorship, critical behavior, and singularities may be expected from combining analytic calculations with simulations from computational gen- eral relativity. Analytic work on new formulations of Einstein's equations may benefit numerical relativity and quantum gravity. Insights from pure mathemat- ics will be helpful here, for example in understanding such issues as the long-time behavior of solutions of Einstein's equations. Key Questions Gravity governs the structure of the universe on the largest scales of space and time. Gravity is the weakest of the four fundamental forces, but it is univer- sal, long range, and unscreened. Cosmology and gravitational physics are thus inextricably linked. An understanding of gravity is necessary to understand the universe, and cosmology provides an arena for testing theories of relativistic gravitation. Cosmology is the subject of a separate document, Cosmology: A Research Briefing (National Academy Press, Washington, D.C., 1995), which is part of this decadal survey of physics. It is therefore not necessary for this report to aim at a

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 67 description of all of cosmology, nor would it be possible in this brief compass. These are the key questions for gravitational physics in this area: . Is Einstein's theory right on the largest scales? Is the big bang model the correct description of our universe? · What is the origin of the fluctuations that grew to form galaxies? · What is the shape and fate of the universe? · What is the universe made of? · What is the value of the cosmological constant? · How did the universe begin? Cosmology: The Basic Facts An increasingly detailed, reliable, and consistent web of observations has given scientists a broad-brush picture of the structure of the universe on the largest scales that can be observed and to the longest times that can be extrapo- lated. These include the observations of the distribution of the galaxies in space (called the large-scale structure), the temperature of the cosmic background radiation, and the primordial abundances of the elements. The basic facts about the universe that emerge from these observations are as follows (see Box 3.2~: · Galaxies are the basic building blocks of the universe. The distribution of these gravitationally bound collections of gas and billions of stars is homoge- neous (the same in one place as in any other) and isotropic (the same in one direction as in any other) when averaged over distance scales above several hundred million parsecs. On smaller scales, galaxies are clustered into groups, filaments, clusters, and superclusters. But in the large, the present universe is much the same in one place as in any other. (One parsec (pc) is roughly 3 light- years or 3 x 10~6 meters. The nearest stars are roughly 1 parsec from the Sun. One megaparsec (Mpc) is 1 million parsecs. The nearest large galaxy is about half a megaparsec away. The size of the visible universe is about 3000 megapar- secs.) · The universe is expanding. The galaxies are receding from one another with a speed v which is related to the distance d that separates them by v = Hod where Ho is the Hubble constant, 70 + 10 km/s per Mpc. Because of this expan- sion, light from distant galaxies is redshifted to a longer wavelength. Since light travels at a finite speed, observations of distant (large-redshift) objects reveal their appearance in the distant past. · The early universe was simpler than the universe today. It was more homogeneous, more isotropic, and more nearly in thermal equilibrium. The variations in the temperature of the cosmic background radiation in different directions the earliest structure that we can see are only a few parts in a million.

68 26~ EVIDENCE FOR THE BIG BANG Fraction of critical density 0.01 0.02 0.05 _ . . I i 0.25 0 24 10-' 10 ' 10 ' -11 !:::::::::::::. . . . , t _ _ 3He I- ~ . \ / _ it ] 1 . d ~ Light Element Abundances As the expanding universe cooled, chemical elements condensed out of the primeval plasma with predictable relative abundances. The observed abundances of the light elements agree well with these predictions, providing one of the most compelling pieces of evidence for the big bang. Quantum gravity ~ = , ? ~ Inflation? 10-35 s 10-43 s CMB Spectrum If matter in the universe was compressed in the big bang, it would have been hot, and would radiate like a hot blackbody. Today we see that radiation in the cosmic microwave background (CMB) radiation, much cooled by the expansion of the universe, with the predicted blackbody spectrum. The CMB is the light from the big bang. (The actual data measurements are shown in this figure; the error bars are smaller than the width of the blue line, which indicates the predicted blackbody spectrum.) ~ 1.0 a) I) u' 0.8- c~ 0.6 0 0.4 - u' 0.2 24 22 GO 20 .2 C7 a GO 18 1 6 ~ 14 _ Calan, (Haml ~ A.J. 1! 0.02 CMB pro Nucleosynthesis - ~ ~106ye 1-10 minutes 1.2 1 1 l 0 5 10 15 20 Waves / centimeter / / / ,

5 20 69 26 24 22 20 C7 Al 18 16 14 T r r I I r rll T r r r r r rll IF .~ Calan/Tololo ¢,~ (Hamuy et al, A.J. 1996) i' ~ 1 0.02 .k 1 1 1 1 1 1 1 1 0.05 0.1 CMB produced ~ - 106years~ For 1 1 1 0.2 redshift z (MA) = :: : .: ::.., (o, o) , -.., .:.:.,, (1, a) . ..-.. :~.-. (2, O) ., o -:''' 11 .... ~ 1 1 1 1 1 0.5 1.0 Expanding Universe The redshift of a galaxy is a measure of the speed at which it is receding from us. A plot of effective apparent magnitude (ma; a measure of relative distance) versus redshift (z) shows that the universe was expanding from a compact state approximately 13 billion years ago, i.e., the big bang. Deviation from a straight line at large redshift measures whether the expansion is slowing down or speeding up. Today CMB Fluctuations The universe at the big bang was almost perfectly smooth, but it must have contained the seeds that condensed by gravity to evolve into today's galaxies. These seeds are seen in tiny 30-millionths-of-a-degree fluctuations in the temperature of the cosmic microwave background shown here as different colored regions in a map of the sky. BOX 3.2 Evidence for the Big Bang. SOURCES FOR FIGURES: Light element abundances- Scott Buries, University of Chicago (Buries, S., et al., 1999, Physical Review Letters, 82, 4176- 4179); expanding universe-Saul Perlmutter, Lawrence Berkeley National Laboratory (Perlmutter, S., et al., 1999, Astrophysical Journal, 517, 565-585); CMB spectrum, CMB fluctuations-NASA's Goddard Space Flight Center and the COBE Science Working Group.

70 GRAVITATIONA:L PHYSICS: EXPLORING THE STRUCTURE OF SPACE AND TIME The Intersection of Gravitational Physics and Cosmology These basic observations, when combined with general relativity, give a powerful theoretical framework for understanding both how the universe is struc- tured and how it evolved to be that way. Modern cosmology lies clearly within the realm of strong gravitational physics. The strongest curvatures in the uni- verse occur in the initial big bang. Some of the places where gravitational physics and cosmology intersect most strongly are described below. The Evolution of the Universe. When the observed approximate symmetries of homogeneity and isotropy are enforced exactly, Einstein's theory predicts the Friedmann-Robertson-Walker (FRW) cosmological models (see Chapter 2~. These models are characterized by only a few parameters. The first is the scale of the expansion rate, which we can take to be the present value of the Hubble constant Ho. The other important parameters are the present-day energy densities in matter and radiation, usually expressed as the ratios Qm and Qr respectively, of their values to the critical density required to close the universe. In addition, there is the value of the cosmological constant A. A cosmological constant could arise from many sources, including the energy of empty space (the vacuum). The value of the cosmological constant is important not only for classical gravity and cosmology, but also for quantum gravity. The smallness of the cosmological constant (less than 10-~28 in the Planck units that characterize quantum gravity; see Chapter 2) remains a mystery whose resolution likely awaits the development of the "final theory" uniting quantum theory with gravity. As mentioned above, our observations of the distant universe reveal its past. Detailed observations of the properties of galaxies at different distances should thus determine the parameters of the best-fit FRW model that describes the evolution of the universe in time and also should measure the value of the cosmo- logical constant. With sufficiently detailed observations the FRW parameters would be overdetermined so that it would then be possible to check whether the FRW models are correct, that is, to test Einstein's theory on this largest of possible scales. The Growth of Inhomogeneities. Galaxies, clusters of galaxies, and the voids and filaments in their observed distributions are examples of inhomogeneities in the universe. The anisotropies in the background radiation are evidence of the progenitors of these present inhomogeneities seen at a much earlier time. The prevailing opinion is that all of today's inhomogeneities grew by gravitational attraction from tiny quantum deviations from the smoothness of the early uni- verse. Different theories for the origin of the structure and the composition of the universe make different predictions for the spatial distribution of galaxies and clusters of galaxies as well as for the statistical properties of the microwave background. By comparing observations of these inhomogeneities and anisotro

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 7 pies to theory, we can test different ideas for the origin of density fluctuations and for the composition and evolution of the universe. Gravitational Lensing. The gravitational attraction of a mass will deflect the course of a passing light ray. This prediction of general relativity was one of the first to be tested observationally in 1919 when Eddington observed the gentle deflection of starlight by the Sun. Much stronger examples of the same phenom- enon are now known. A large concentration of mass can act as a lens producing one or more images of a source behind it. (See Figure 3.7.) For example, more than a dozen quasars tensed by intervening galaxies have been observed. The tensing of quasars by intervening galaxies not only provides a dramatic FIGURE 3.7 An image of multiple arcs in galaxy cluster 0024+1654, taken by the Hubble Space Telescope. The mass in the foreground cluster (the bright clustered ob- jects) acts as a gravitational lens and distorts the shape of background galaxies into arcs. The cluster lens is so powerful that it produces five images of the same galaxy. (Courtesy of J. Anthony Tyson, Lucent Technologies, Wesley N. Colley, Harvard-Smithsonian Cen- ter for Astrophysics, Edwin L. Turner, Princeton University, and NASA.)

72 GRAVITATIONA:L PHYSICS: EXPLORING THE STRUCTURE OF SPACE AND TIME confirmation of one of the predictions of Einstein's theory but also in principle allows the verification of its predictions for the propagation of light in cosmologi- cal spacetime geometries. There are three major roles that lenses play in cosmol- ogy: · Determining the distribution of matter in galaxies and clusters. A gravi- tational lens distorts and amplifies background images by amounts that depend on the quantity of imaging mass and the distances to the source and lens. Weak tensing observations of galaxies and quasars can therefore be used to map the distribution of matter in galaxies and clusters. · Measurement of cosmological parameters. If the foreground cluster or galaxy is a powerful enough lens, it can produce multiple images of the same source. The light's travel time for the different images can differ by several hundred days and depend upon the mass of the lens and the distances to the source and lens. Such timing observations allow astronomers to determine dis- tances to tensing systems and thereby to determine the Hubble constant and constrain other cosmological parameters, especially the cosmological constant. · Determining the nature of the dark matter. By observing stars in nearby galaxies and looking for "microlensing events" produced when a massive object passes between Earth and a star, astronomers can detect such massive compact objects in the neighborhood of our Galaxy. Gravitational Waves from the Early Universe. The early universe is a source of gravitational radiation. Many of the theoretically proposed processes that might have shaped the evolution of the early universe produce a gravitational wave background that is potentially detectable today. Inflation parametrically ampli- fies quantum fluctuations in the geometry of spacetime to produce a gravitational wave background. Gravitational radiation is an important mode of decay of cosmic strings topological defects formed in phase transitions in the early uni- verse. Collisions of bubbles produced in any phase transition at the end of an inflationary epoch may have been a copious source of gravitational radiation. Each of these processes leads to a gravitational wave background with a charac- teristic amplitude and non-thermal spectrum today. The observation of any of these gravitational wave backgrounds would be of enormous importance for cosmology because it would give us a picture of the universe at a much earlier stage than any available in electromagnetic radiation. The electromagnetic back- ground radiation originated about 300,000 years after the big bang when the universe became transparent. By contrast, gravitational radiation interacting much more weakly may have originated as early as 10-22 seconds after the big bang. Quantum Cosmology. Cosmology presents a problem that is fundamentally different from those encountered elsewhere in physics. This problem is the need

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 73 for a theory of the initial condition of the universe. The familiar laws of physics, such as Newton's second law, Maxwell's equations, or the Einstein equation, describe evolution in time. Such dynamical laws require boundary conditions to yield predictions, and the Einstein equation governing the evolution of the uni- verse is no exception. Usually boundary conditions summarize observations of the part of the universe outside a subsystem whose evolution is being studied. But in the study of the whole universe there is no "rest of the universe." The cosmological boundary conditions must be part of the laws of physics them- selves. A theory of the cosmological boundary condition is as necessary a part of any "final theory" as a fundamental theory of the laws governing evolution in time. In a quantum theory, a theory of the initial condition of the universe is a theory of its initial quantum state. That is why the area of astrophysics concerned with this initial condition is called quantum cosmology. What is the quantum state of the universe? Does it arise from a fundamental principle that explains the simplicity of the early universe revealed by observations? Is it connected with the fundamental dynamical theory? These are the kinds of questions quantum cosmology seeks to answer by working at the intersection of the disciplines of cosmology, quantum mechanics, and quantum gravity. In quantum cosmology the physics of the universe's largest scales are united with the physics of its very smallest. Achievements Tests of the Big Bang Model NASA's Cosmic Background Explorer (COBE) satellite measured the en- ergy distribution of the microwave background radiation. COBE showed that this distribution was thermal to an accuracy of 1 part in 10,000. A thermal spectrum is one of the fundamental predictions of big bang theory. Since alterna- tive cosmological theories have not been able to explain the existence of this nearly uniform thermal energy, this observation has become one of the pillars of the big bang picture. Astronomers have measured the redshifts to more than 100,000 galaxies, a more than 10-fold increase in the past decade. They found that the galaxy distribution is clustered on scales as large as 100 million parsecs. On even larger scales, the distribution of galaxies appears to be uniform. These observations finally confirmed that the universe is nearly homogeneous on large scales much the same in one place as in any other. With a successfully repaired Hubble Space Telescope and the new Keck 10-meter telescopes, astronomers have been able to observe galaxies at high redshift. These have lower abundances of carbon, oxygen, and iron, elements that are produced through stellar evolution, and also are more irregular in shape

74 GRAVITATIONA:L PHYSICS: EXPLORING THE STRUCTURE OF SPACE AND TIME and show much more evidence of star formation. Thus, as predicted in the big bang model, the distant galaxies appear younger. Observations of Primordial Fluctuations The COBE satellite also detected very small directional variations in the temperature of the microwave background of only 30 millionths of a degree. (See Figure 3.8.) These observations directly probe the distribution of matter only 300,000 years after the big bang, the moment when electrons and protons first combined to form hydrogen, and the universe became transparent to most elec- tromagnetic radiation. Ground- and balloon-based microwave background ex- periments have confirmed the COBE result and detected additional fluctuations on smaller angular scales. Estimates of the Size of the Universe Astronomers have significantly improved determinations of the size, den- sity, and geometry of the universe. The Hubble Space Telescope has monitored FIGURE 3.8 COBE's map of the microwave sky. The entire sky is shown in this false- color map in galactic coordinates. Radio emission from gas and dust in the disk of our own Galaxy appears as a strip across the middle of the map. Away from this strip, the fluctuations are due to tiny variations (1 part in 100,000) in the temperature of the cosmic background radiation. If the inflationary model is correct, these fluctuations have their origins in processes that occurred 10-36 seconds after the beginning of the big bang. (Courtesy of NASA's Goddard Space Flight Center and the COBE Science Working Group.)

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 75 variable stars in nearby galaxies whose well-established relation between their period of variability and their intrinsic brightness allows them to be used to measure the distance to nearby galaxies and to infer the Hubble constant, Ho (the expansion rate of the universe). Measurements of the motions of galaxies en- abled astronomers to infer the mean density of the universe. While the data is not yet definitive, these measurements suggest that the density of the universe in matter is not enough to stop the expansion of the universe. Astronomers are also using Type Ia supernova explosions in distant galaxies to probe the geometry of spacetime. These observations also suggest that the universe will expand forever and even accelerate its present expansion. Dark Matter Astronomers can measure the mass of galaxy and galaxy clusters through a variety of techniques. All of these techniques find that the gravitational mass of a galaxy exceeds the mass in luminous stars by at least a factor of 10. Astronomi- cal searches had ruled out cold gas, warm gas, hot gas, and dust as possible candidates for this mysterious dark matter. In the past few years, gravitational microlensing searches have ruled out two other candidates planets and brown dwarfs (bound objects with masses greater than Earth's but less than 8 percent of the mass of the Sun) as possible dark matter candidates. Origin of Elements and the Number of Light Neutrinos The big bang model successfully explains the origin of primordial deute- rium, helium, and lithium. These light elements were produced in the first min- utes of the universe. Heavier elements such as carbon, oxygen, and iron were produced subsequently by nuclear burning in stars. The big bang explanation for the abundances of deuterium and helium fits the data only if there are no more than three light neutrinos. During the past decade, measurements of the proper- ties of the Z boson at CERN (the European Laboratory for Particle Physics) successfully confirmed this prediction. The Inflationary Paradigm Over the past 15 years, cosmologists developed the inflationary universe paradigm, amalgamating ideas from cosmology and particle physics. This exten- sion of the big bang theory posits an early epoch in which vacuum energy drove an ultrarapid expansion of the universe. This rapid expansion inflated a tiny region of space into the entire part of the universe visible today, smoothing any primordial variations in the geometry of space, and driving the density of the universe toward the critical density required for closure. The inflationary para- digm goes far toward explaining the homogeneity, large size, and age of the

76 GRAVITATIONA:L PHYSICS: EXPLORING THE STRUCTURE OF SPACE AND TIME universe. Because of initial quantum fluctuations, inflation proceeds at slightly different rates in different regions of the universe, generating spatial variations in its density, and in turn, these weak density fluctuations produce temperature variations in the microwave background that are seen by COBE (see Figure 3.8~. These fluctuations eventually grow through their own self-gravity to form galax- ies, clusters, and other large-scale structures that we see today. The specific predictions of the inflationary scenario depend on the compost lion of the universe and the details of particle physics. In studying inflation, cosmologists tie together and test ideas from grand unified theories and from quantum gravity. Over the past 20 years, theorists have developed the conceptual and numerical tools needed to make detailed quantitative comparisons of the variants of the inflationary model with the data, primarily the distribution of galaxies. By the mid-1980s, cosmologists realized that models in which most of the matter in the universe was in the form of neutrinos (generically called "hot" dark matter) were not consistent with the large-scale structure observations. The "cold" dark matter model, which posited that galaxies grew from inflationary fluctuations in a critical density universe filled with weakly interacting massive particles, emerged as the standard theory for the origin of structure. While this model can fit the basic qualitative features of the microwave background data, it cannot consistently fit the detailed quantitative features of the large-scale struc- ture and the microwave background data. Nor can the current data be fit by models of structure formation in which phase transitions in the early universe generate topological defects that seed the formation of galaxies and large-scale structure. The currently most successful models of structure formation are inflationary models with a subcritical density of matter. These low-density-universe models either posit the existence of a cosmological constant to make the universe flat or posit a modified form of inflation that produced a negatively curved universe. Either way, they suggest the existence of new physics. . Opportunities In the coming decade astronomers and physicists will acquire a wealth of new data that will enable testing and refinement of current ideas and, perhaps, lead to new models for the origin of the universe. Precision Cosmological Measurements The U.S.-led Sloan Digital Sky Survey and the Anglo-Australian 2DF project will measure the redshifts of more than 1 million galaxies and quasars, a 10-fold increase in the number of measured redshifts over that available today. These observations will enable astronomers to quantify to new accuracy the level of inhomogeneities in the galaxy distribution. Observations of gravitational tensing

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 77 of distant galaxies and clusters will also directly quantify the level of inhomoge- neities in the mass distribution. NASA's Microwave Anisotropy Probe (MAP), which is scheduled for launch in late 2000, and the European Space Agency's Planck Surveyor, which is sched- uled for launch in 2007, will map the microwave background radiation across the whole sky with angular resolution 30 to 60 times better than that obtained with the COBE satellite. These microwave background observations will measure the level of inho- mogeneities in the universe 300,000 years after the big bang. The combination of these data sets will enable astronomers to describe the statistical properties of density fluctuations and their evolution with very high precision. Inflationary theories make very specific predictions for the statistical proper- ties of the microwave background fluctuations and for the statistical properties of the density fluctuations traced by galaxies. This confluence of experimental accuracy and theoretical calculability will enable cosmologists to finally answer some of the fundamental questions that span astrophysics, gravitational physics, and particle physics: . What is the origin of the fluctuations that grew to form galaxies? Infla- tion makes very specific predictions for the microwave background. If they are confirmed, then this will be a major success for the inflationary paradigm. If the upcoming observations are not consistent with the inflationary model, then we will need to find an alternative theory for the origin of the universe. · What is the shape andfate of the universe? By measuring the character- istic angular size of a typical hot spot in the microwave background, we can measure the geometry of the universe. The physical diameter of the spot is fixed by the speed of light and the age of the universe when electrons and protons combined to make hydrogen, and so is related to the geometry. In turn, general relativity directly relates the geometry of the universe to the density of matter and the value of the cosmological constant. · What is the universe made of? By measuring the characteristic intensity profile of the typical hot spot, we can measure the sound speed in the early universe. The sound speed depends on the ratio of density in electrons and protons to density in radiation, a central number in cosmology. By measuring the characteristic physical scale of galaxy clustering, we can determine the ratio of energy density in matter to the energy density in radiation, a central cosmological parameter. · What is the value of the cosmological constant? By measuring the relative amplitude of temperature fluctuations and matter fluctuations as a function of size, we can measure the rate of growth of gravitational fluctuations. This growth depends sensitively on a combination of cosmological parameters, particularly the cosmological constant and the nature of the dark matter.

78 GRAVITATIONA:L PHYSICS: EXPLORING THE STRUCTURE OF SPACE AND TIME There are several ongoing complementary approaches to answering these cosmological questions. Large-scale structure observations measure the distribu- tion of galaxies and their motions. Lensing observations measure the statistical properties of dark matter. Microwave background observations measure the distribution of matter and radiation in the early universe. Type Ia supernovae, which have already been detected out to large redshifts, can be used to measure the cosmological constant through the luminosity-redshift relation. Gravitational lenses, which probe the angular distance-redshift relation, will provide another opportunity to measure this important parameter. If all the observations agree, then astronomers may have measured a number that might be predicted by the correct quantum gravity theory. . Is Einstein's theory right on the largest scales? This wealth of data can also be used to test Einstein's equations on the largest of possible scales. If the FRW model is indeed the correct cosmological model, then different techniques will yield consistent values for cosmological parameters and thereby will verify general relativity on the largest possible scales. Probing the Composition of the Universe In the coming decade, laboratory techniques should achieve the sensitivity needed to detect supersymmetric dark matter (a kind of cold dark matter) in underground direct detection experiments. Neutrino telescopes will search for high-energy neutrinos produced through the annihilation of supersymmetric par- ticles trapped in Earth and the Sun. A detection will have profound implications for our understanding of the universe. Particle physicists will test supersymmetry directly at the Large Hadron Collider (LHC). If supersymmetry is not detected at the LHC, the lightest supersymmetric particle will no longer be the most attrac- tive dark matter candidate. If supersymmetry is detected, then measurements of supersymmetric parameters will lead to a prediction of its cosmological abun- dance. With the use of larger telescopes and larger cameras, gravitational lens mea- surements will also be able to characterize the distribution of mass in our own Galaxy. Microlensing experiments have already detected tens of tensing events, whose nature is a mystery. In the coming decade, astronomers will likely detect hundreds more. With this much larger data set, astronomers should be able to uncover the nature of the tensing objects and determine if they make a significant contribution to the total mass of our Galaxy. Windows onto the Beginnings of the Universe Observation. The development of LIGO and other ground-based detectors, along with a future space-based interferometer, will open a new window into the earli

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 79 est moments of the big bang. As described more fully in the "Key Questions" part of this section, there are a number of potential sources of gravitational radiation in the early universe rapidly varying fields during inflation or another phase transition, for example. Such sources could produce a gravitational wave background potentially detectable by the methods described in Section I of this chapter. Our understanding of the physics of the universe when these waves were formed is primitive, so we cannot as yet predict with any confidence the expected amplitude of this signal. However, if the universe did begin with violent physics, then the gravitational waves will bear the imprint of these first moments. That makes their detection interesting even if it is not clear whether this is an opportu- nity for the next decade or future ones. It is reasonable, therefore, to search for these probes of the earliest instants of our history over as wide a spectrum of wavelengths as possible with existing instruments. Even upper limits in a range of wavelengths can provide important constraints on early-universe physics. Theory. Several promising theoretical directions may lead to a deeper under- standing of the origin of the universe and its basic physical laws. The continued development of non-perturbative formulations of string theory and canonical quantum gravity (see Section V of this chapter) will give, for the first time, workable quantum theories of gravity that can be applied with confidence to the quantum era of the universe's evolution and will provide a framework for formu- lating and exploring theories of the initial condition. Quantum cosmology offers the prospect that, in the next decade, we may not only understand how the universe is structured on the largest scales of space and time, but also begin to understand, as a basic law of physics, why it is the way we see it today. Key Questions Einstein's gravitational theory is more than 80 years old, yet until the 1960s, there was only modest progress in testing it. This was due to the fact that, for the majority of physical systems so far accessible to careful measurement, its pre- dictions differ from those of standard Newtonian gravity by only minute amounts. Consequently, testing the theory has always been a challenging task. Only in the past few decades have truly precise tests been made possible by the rapidly evolving technology of high-precision measuring tools, such as atomic clocks, lasers, radio telescopes, and torsion balances. At the same time, theoreti- cal advances have made it possible to understand clearly the observable predic- tions of the theory, and to compare and contrast them with possible alternative theories.

80 GRAVITATIONS PHYSICS: E~LOHNG THE STRUT OF SPACE ED TIME Despite great progress on both the experimental and theoretical fronts, key questions remain open: . How "right" is general relativity? Will further experimental tests con- tinue to agree with the theory, or will a deviation appear at some level? · If a deviation appears, will that signal a new theory of gravity, new physi- cal interactions, or new elementary particles? The possibility of new physics is not idle speculation; it is motivated by today's searches for theories of the fundamental interactions. For example, string theory suggests that general relativity will fail at some level, although the level is not yet predictable. One result of this failure would be a violation of the principle of equivalence (see Box 3.3~. Another connection is through the cosmological constant. Observations explained by a cosmological constant might also be explained by an evolving, low-mass scalar field (although the "constant" would then be time dependent). Such a scalar field might very well show up in tests of the equivalence principle. Thus, although many actual experiments will take place under conditions of weak gravity, they will be searching for the imprints there of physics at strong gravity scales. Detection of such imprints would be a profound discovery. Achievements Prior to 1960, the empirical basis of general relativity consisted of the body of evidence supporting special relativity, experiments that verified the principle of equivalence underpinning general relativity, and two experiments that checked the theory itself: the deflection of starlight and Mercury's perihelion advance. The latter two experiments were regarded as being good to accuracies only be- tween 10 and 50 percent. Since 1960, dramatic progress was made, both in improving the precision of existing tests and in performing new high-precision tests. Here the COP focuses on developments that have occurred since the release of the last decadal survey (Gravitation, Cosmology, and Cosmic-Ray Physics, National Academy Press, Washington, D.C., 1986~. Tests of the Universality of Free Fall Improved tests were performed of the equality of acceleration of different bodies, or the universality of free fall (UFF), which served as the inspiration for the equivalence principle. This principle is the foundation for the geometric theories of gravity like general relativity. From a quantum viewpoint, it is a very special consequence of theories in which the force is produced by a spin-two graviton. New spin-zero and spin-one particles and their couplings that are

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 8 BOX 3.3 Einstein's Principle of Equivalence Einstein generalized the feature of Newtonian mechanics that all bodies in a gravitational field fall with identical accelerations, into a guiding principle for his relativistic theory of gravity. If all objects have the same acceleration, gravitational effects are equivalent to an acceleration of the frame of reference. Thus a freely falling observer will find that gravitational effects disappear. In Newtonian terms, this is a consequence of the exact equality of the inertial mass (the mass in F= ma) and the gravitational mass (the mass in F= GMm/r2). This equivalence principle, or universality of free fall (UFF), leads directly to many of the celebrated predic- tions of general relativity such as the existence of spacetime curvature, and the gravitational redshift of clocks. The UFF is a special property of general relativity and is expected to be violated by quantum mechanical forces that typically arise in unified field theories. Because of the deep importance of the equivalence principle, and the possibil- ity that UFF violation could be used to discover new tiny forces, the UFF has been tested in a number of ways. Precise tests compare the gravitational accelerations of different test bodies in the field of attractors such as the Sun, Earth, local topog- raphy, laboratory-scale movable masses, and the dark matter in our Galaxy. The most sensitive experiments use torsion balances (see Figure 3.9) that produce no signal when two different types of test bodies have identical accelerations. Cur- rently, torsion balances and lunar laser ranging are able to compare accelerations with a precision of 5 x 1 0-13 cm/s2. An object starting 2000 years ago from rest with a constant acceleration of 5 x 1 0-13 cm/s2 would now be moving at the same speed as the end of the minute hand on a wall clock. Other measurements of extraordinary precision have been exploited to test that gravitational self-energy itself obeys the UFF. Gravitational self-energy is completely negligible for laboratory-sized objects; even for objects the size of Earth and the Moon it is very small only 46 parts and 2 parts in 1011, respectively. Earth and the Moon also differ in that Earth has an iron-nickel core, whereas the Moon does not. The relative accelerations of Earth and the Moon toward the Sun have been extracted from the lunar laser-ranging data, while the relative accelera- tions of test bodies with "Earth-like" and "Moon-like" compositions have been checked using torsion balances, permitting possible violations of UFF by gravita- tional self-energy to be isolated. None was found down to the level of about 2 parts in 1000. typical of unified theories (such as string theory) produce violations of the equiva- lence principle at some level and length scale. Tests of the UFF reached the level of a part in 10~2 and attained sufficient sensitivity to demonstrate that the interaction of ordinary matter with galactic dark matter obeys the UFF to a part in 1000. Many laboratory experiments of this type performed since 1986 were done specifically to search for new forces pre- dicted by theories of the elementary particles or by string theories. Ongoing laser ranging to corner reflectors on the Moon provided ever improving tests of the

82 GRAVITATIONAL PHYSICS: EXPLORING THE STRUCTURE OF SPACE AND TIME FIGURE 3.9 Torsion pendulum used to test Einstein's equivalence principle for test bodies attracted by Earth, the Sun, and the dark matter in our Galaxy. The pendulum is small (its over- all diameter is about 3 inches) to minimize dis- turbing effects from local variations in the grav- itational force. It hangs from a tungsten fiber that is so thin that it cannot be seen in the pho- tograph above. The circular plate holds four cy- lindrical test bodies (two of copper and two of beryllium) along with four right-angle mirrors (see inset) that are part of a sensitive optical system for detecting pendulum twists. The an- nular ring underneath the pendulum is a "safety net" to catch the pendulum should a small earth- quake shake the apparatus and break the sus- pension fiber. The pendulum is suspended in a vacuum and the entire instrument is rotated continuously at about one revolution per hour. A violation of the equivalence principle would show up as a pendulum twist that varied at this rotation frequency. (Courtesy of Eric Adelberger and the Eot-Wash Group, Universi- ty of Washington.)

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 83 equality of acceleration of the Moon and Earth toward the Sun, to a level today that is actually slightly better than that from laboratory experiments. The lunar results also verified to a part in 1000 that bound gravitational energy within Earth and the Moon falls with the same acceleration as mass and other forms of energy, providing a direct test of general relativity. Another test of the equivalence principle was made possible by techniques developed within atomic physics, such as atom and ion traps, and laser cooling, which were used to put exquisitely stringent constraints on any anisotropy, or preferred direction, in local physics that might be generated by new cosmic interactions. Pulsar Tests of Relativistic Gravity The Hulse-Taylor binary pulsar provided a definitive test of the existence of gravitational waves, in agreement with the prediction of general relativity to a third of a percent. Because the stars in the binary pulsar system are neutron stars, with strongly relativistic, nonlinear internal gravitational fields, the observations also provided indirect support for the theory in the strong-gravity regime. Tests of the UFF, of momentum conservation, and of anomalies related to a hypotheti- cal preferred cosmic reference frame were also performed using binary pulsars and millisecond pulsars. Search for Frame Dragging The last decade also witnessed the development of a number of approaches to measuring the twisting up of spacetime in the vicinity of rotating bodies, known as the dragging of inertial frames, or the Lense-Thirring effect. This effect has not been measured directly to date, although aspects of it are implicit in other observed relativistic effects, such as lunar and planetary motion, and the motion of the Hulse-Taylor binary pulsar. Not only is this effect important as a prediction of general relativity, but it also has deep conceptual implications for the meaning of absolute rotation. Furthermore, the forces associated with frame dragging are thought to play an important role for jets of matter that are seen being ejected from quasars and active galactic nuclei, coming from the rotating, supermassive black holes believed to reside there. The main ongoing project to measure frame dragging accurately is the NASA Relativity Mission, informally known as Gravity Probe B. in which gyroscopes are to be placed in orbit around Earth and their processions relative to distant stars measured. (See Box 3.4.) This experiment is expected to measure the Lense- Thirring frame-dragging effect to a precision of about 1 percent. It will also measure the larger geodetic precession caused by space curvature around Earth to a precision that could reach a thousandth of a percent. The project was conceived and begun in the 1960s. Since the release of the last decadal survey of

84 GRAVITATIONS PHYSICS: E~LOHNG THE STRUCTURE OF SPACE^D TIME BOX 3.4 Gravity Probe B Gravity Probe B (GP-B) is a space project to measure the tiny precession of gyroscopes relative to distant stars. The precession is induced by the twisting of spacetime caused by the rotating Earth (dragging of inertial frames) and by the curvature of space around it. The satellite is scheduled for launch in 2000. The G P-B gyroscopes are spheres of fused quartz, 1.5 inches in diameter. Each gyro- scope is electrically suspended by applying voltages to saucer- shaped electrodes in the two halves of the housing. It is spun up to 150 Hz by gas run- ning through a channel in the right-hand hemisphere, after which the gas is pumped out and the ball runs freely in a vacuum. The direction is read out by a superconducting quantum-interference device (SQUID) connected to the superconducting circuit on the face of the left-hand hemisphere. (Photo- graph courtesy of Ms. Denise Freeman.) The GP-B spacecraft will hold a dewar for liquid helium (the main body of the spacecraft shown), with the probe containing the gyro- scopes inside. At the upper left is the telescope assembly that will establish a reference direction to a distant star against which to measure the gyroscope pre- cessions. Also visible are solar panels for power. (Courtesy of Lockheed Martin Missiles & Space.)

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 85 . . physics in 1986, the project has made substantial technological progress and secured the support of NASA through launch and data analysis. At present, the spacecraft is built, construction and installation of the flight experimental hard- ware is complete, and the project is proceeding toward a proposed launch in 2000. For the purpose of this report, Gravity Probe B is treated as part of the committed, ongoing program in gravitational physics. Re-emergence of Scalar-Tensor Theory An important theoretical development of the last decade was the re-emer- gence of scalar-tensor gravitational theory as an alternative to general relativity. Scalar-tensor theories augment the standard tensor gravitational interaction of general relativity with a scalar field. Their exemplar, the Brans-Dicke theory, fell into disfavor during the 1970s, as experiments strongly pointed toward general relativity. But a new class of more general scalar-tensor theories was a product of developments in particle theory, specifically string theory (see Section V of this chapter), where the presence of scalar fields (spin-zero particles) in addition to the tensor (spin-two) metric is required. In many string-inspired models, the "low-energy" limit (appropriate for everyday gravity, astrophysics, and most of cosmology) is necessarily a scalar-tensor theory. In many such models, standard cosmological evolution drives the parameters of the scalar-tensor theory toward, but not quite to, those of general relativity. This permits such theories to agree closely with general relativity in weak-field situations, such as the solar system, while diverging strongly from it in early-universe and strong-field situations. The differences for weak fields, while perhaps no more than a part in 105, may be sought with experiments, such as Gravity Probe B's proposed measurement of the geodetic precession, or improved tests of the equivalence principle. This conjunction between particle theory and gravity in scalar-tensor gravity is an opportunity for further theoretical study and future experimental tests. Applications of Relativistic Gravity A surprising development since the decadal survey in 1986 is the extent to which a number of general relativistic effects have taken on practical signifi- cance. In the Global Positioning System (GPS), a high-precision navigational and time-transfer system that is the basis for a multibillion-dollar commercial industry, the relativity of time plays a crucial role (see Box 2.1 in Chapter 2~. The effect of gravity on the rates of clocks (the gravitational redshift), together with the special relativistic time dilation due to the clocks' motion, results in a differ- ence between the rates of the atomic clocks on the 24 orbiting satellites of the GPS and those of clocks on the ground. If the accumulated difference in time, almost 40 milliseconds per day, were not taken into account, the GPS could not

86 GRAVITATIONS PHYSICS: E~LOHNG THE STRUCTURE OF SPACE ED TIME meet its stated navigational accuracy of 15 meters, or its time transfer accuracy of 100 nanoseconds. Relativistic corrections are routinely incorporated into computer modeling of the orbits of interplanetary spacecraft, and into analyses of Earth's gravity field from precisely tracked terrestrial orbiters. Another relativistic effect that has been put to use is the deflection of light, in this case as an astronomical tool. When light from a distant object passes by or through a galaxy or cluster of galaxies, the gravitational light deflection can produce multiple images of the distant object, arc-like distorted images, or com- plete ring-like images. Careful study of these images can provide a map of the mass distribution in the tensing system, and it plays a role in the search for dark matter and the measurement of cosmological parameters. An analogous phenom- enon is microlensing, in which a foreground mass passes in front of a distant star, augmenting its intensity momentarily through gravitational focusing. This effect has also been used extensively in searches for dark objects in and around our own Galaxy. (See Section III of this chapter.) Opportunities The opportunities described here are necessarily of an open-ended, explor- atory character. Scientists seek evidence that current theories might be breaking down, revealing clues to new physics beyond their limits of applicability. It is impossible to predict with any confidence what sensitivity will be required in these experiments. But it is not unreasonable to expect that one or more of these lines of research will reveal evidence that new theories must replace or augment the current ones. If this happens, the impact of such a discovery will likely be revolutionary. Tests of the Equivalence Principle A key opportunity for the coming decade in experimental gravity will be the testing of fundamental aspects of the gravitational interaction in search of, or to constrain, new physical interactions. The interactions inspired by the particle physics-gravity connection generally produce violations of the UFF, violations of the gravitational inverse square law, and spin-dependent gravitational interac- tions. Existing laboratory tests of the UFF are still far from reaching the ultimate limitations of the technique and can reasonably be expected to improve by a factor of at least 50. A space test of the UFF could achieve a millionfold im- provement over current levels, reaching a part in 10~8, by monitoring the relative motion inside a satellite of two freely moving bodies of different materials. During a year-long mission, this amounts to thousands of repetitions of Galileo's famous experiment. The principal advantage of the space environment is the

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 87 substantial reduction of the effects of vibrations that plague ground-based experi- ments. Any additional "gravitational" quanta that are spinless (such as the dilator and moduli of string theory) would violate the gravitational inverse square law at some length scale. String theory and other models that endeavor to unify the interactions are not yet at a stage where they can make a definite prediction for the size of the new effects. But this situation is likely to improve in coming years, and violations at some scale seem inevitable. For example, there is an intriguing recent suggestion that large violations of the inverse square law could occur at the micron scale. Laboratory and astronomical tests made prior to the last decade explored length scales down to 1 millimeter. Attention is now focusing on even shorter length scales. In this regime, the gravitational forces are necessarily weak compared to electromagnetic interactions between neutral objects, so that new techniques are required. It is useful to point out that many of the experimental improvements needed to perform these delicate measurements, such as vibration isolation and sensitive gravity "radiometers, may have payoffs in other areas, such as gravitational wave detection and geophysics. At the same time, this effort will benefit from theoreti- cal progress, which could lead, for example, to more precise predictions from string theory for the strength and range of violations of the UFF or the inverse square law. Search for Frame Dragging Another opportunity that can be realized in the next decade is the detection and study of the effects of frame dragging. The ongoing Gravity Probe B project (see above) is the only experiment capable of a high-precision test of the effect. Current plans call for launch in 2000 and completion of the mission by 2002. Another way to detect frame dragging is to measure the rotation of the orbital plane of a satellite in Earth orbit. This could be accomplished using laser-ranged geodynamic satellites called LAGEOS, albeit at a substantially lower level of accuracy than the goal of Gravity Probe B. Data from the two LAGEOS satellites currently in orbit are being analyzed by various groups, with the goal of under- standing and reducing sources of systematic error. Ideally, the launch of a third LAGEOS satellite with orbital tilt having a prescribed relationship to that of one of the other LAGEOS satellites could provide a "cleaner" measurement, free of some of the error sources. Solar System Tests of Gravitation General relativity is a fundamentally nonlinear theory (gravity begets grav- ity), yet the only experiments in the solar system that test that aspect of the theory are the perihelion advance of Mercury and lunar laser ranging, now known to

88 GRAVITATIONS PHYSICS: E~LOHNG THE STRUT OF SPACE ED TIME agree with general relativity to parts in a thousand. Another test of nonlinearities could be provided by a space experiment in which atomic clocks travel close to the Sun. In such an experiment, the shift in frequency between satellite and Earth clocks, or between satellite clocks of different physical structure, contains not only the first-order, or linear contribution, which could be tested to a part in a billion, but also a nonlinear term, which could be tested to a part in a thousand. Lunar laser ranging has been one of the most cost-effective and scientifically productive projects arising from the space program. It has yielded new informa- tion on the orbit and rotational motion of the Moon and on crustal motions on Earth. It has also verified the equivalence principle for Earth and the Moon and has helped set bounds on a temporal variation of the Newtonian gravitational constant. Improved lasers, better modeling of the lunar motion, and the contin- ued accumulation of data will provide further improvements in all of these areas. For example, the measurement of the equality of acceleration could be improved by an order of magnitude. Binary and Millisecond Pulsars To date, only about 1000 out of a predicted 105 pulsars in our Galaxy have been discovered; of these, 100 could be in binary systems. While continued searches for and observations of millisecond and binary pulsars will be driven by independent astrophysical considerations, they will provide opportunities for fur- ther tests of relativity in the radiative and strong-field regimes. For example, the fortuitous discovery of binary pulsars of the right characteristics, such as systems containing both a pulsar and a black hole, could result in a 10-fold improvement in accuracy in the test of gravitational radiation damping, provide a high-preci- sion measurement of a companion black hole mass, detect the precession of the spin of a neutron star, contribute to a determination of the distribution of neutron star masses, and help sharpen the event rate of inspiraling and coalescing neutron star binaries. The Newtonian Gravitational Constant The Newtonian constant G. which governs the strength of all gravitational interactions, was historically the first "fundamental constant" in physics. Yet today, with an official uncertainty of about a part in 104, it is the least precisely determined of any of these constants. Recently, measurements of G at several laboratories have cast doubt on the accepted value of G and especially on its uncertainty. The next decade will see the completion of G measurements using a wide variety of techniques and devices, such as torsion balances, fountains of ultracold atoms, or gravimeters that see a modulated field, possibly reaching a level of a part in 106. Consistent results from several groups will be needed to give confidence that the systematic errors in the measurements are understood.

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 89 Improved bounds on any temporal variation of G of cosmic origin could help constrain alternative gravitational and cosmological models, such as those arising from string theory. Key Questions There have been three major crises in theoretical physics in this century. In each case, two well-established theories were found to be incompatible, either because they were based on contradictory assumptions about the workings of the physical world, or because they led to physically untenable conclusions. The first was the conflict between Newtonian gravity and special relativity, which was resolved by Einstein's theory of general relativity. The second arose from ten- sion between thermodynamics and electromagnetism, which led to the develop- ment of quantum theory. In both of these cases, the crisis was resolved not by a small modification of one of the theories, but rather by an entirely new funda- mental theory that introduced a new framework and made some old concepts obsolete. Over time, both of these theories passed stringent experimental tests and now form the cornerstones of modern physics. Unfortunately, however, general relativity and quantum theory are themselves mutually incompatible, presenting physicists with a third crisis. It is likely that the resolution of this crises will be as profound as the previous two, yielding a major change in our view of nature. The resulting theory, quantum gravity, is expected to be crucial for under- standing the strongest gravitational fields in the universe. It is possible to make a rough estimate of when the effects of quantum gravity should become impor- tant. This is because, as mentioned in Chapter 2, there is a unique combination of the fundamental constants of general relativity and quantum theory which has dimensions of length, up = (hGIc3~/2 ~ 1 0-33 cm, called the Planck length. When the gravitational field is so strong that space is curved on this scale, then quantum gravity is indispensable. Such extreme conditions were present in the early universe. Our current cosmological models can in principle be extrapolated back to t = up I c ~ 10~3 seconds after the big bang, but then they completely break down. Quantum gravity should provide a description of the first moments after the big bang, and perhaps of the big bang itself. In certain situations, effects of quantum gravity can be important even when the gravitational fields are significantly weaker than the above estimate. In particular this is the case around black holes. It turns out that, because of the unusual properties of space and time near a black hole, when quantum effects are included black holes are not really black; they radiate via a quantum tunneling process, losing their mass and becoming hotter. This radiation can be quite significant. For example, if black holes with mass of the order of 10~5 grams

90 GRAVITATIONS PHYSICS: E~LOHNG THE STRUCTURE OF SPACE ED TIME were formed in the early universe, they would appear today to be white hot and would explode. Some of the key questions in quantum gravity are the following: . How can the principles of general relativity and quantum theory be uni fled into one consistent framework? . · What are the quantum properties of black holes? · What is the nature of space and time at the smallest possible scales? · Is this smallest-scale structure responsible for curing the short-distance infinities of quantum theories of other fundamental forces? · What was the universe like 10~3 seconds after the big bang? As the COP describes below, there has been enormous progress over the past decade in trying to answer these questions, especially the first three. This is due partly to a new formulation of the problem, and partly to the influx of ideas from high-energy physics. As the search for a unified theory of all forces expanded to encompass gravity, particle physicists were naturally led to seek a quantum theory of gravity. The next decade promises to be a very exciting one, in which ideas from different approaches may fuse together, providing deeper insights and per- haps complete answers to these fundamental questions about nature. Achievements The usual formulations of quantum theory require a fixed notion of time since, e.g., quantum states are specified at an instant of time. But in quantum gravity, physicists expect the spacetime geometry to fluctuate. This raises deep conceptual problems, especially in the cosmological context where there are no external observers with clocks. To address such problems, a new route was developed in the l990s; quantum theory was generalized to accommodate quan- tum spacetime geometry. Usual quantum mechanics is recovered in those epochs and situations in which the spacetime geometry is approximately classical. This conceptual advance resulted from a fruitful interchange of ideas between experts working on quantum gravity, quantum theory of closed systems, and foundations of quantum mechanics. In spite of this progress in constructing a framework, however, the task of actually constructing a quantum theory of gravity remains formidable. Straight- forward quantized general relativity is "perturbatively non-renormalizable" it yields infinite answers to physical questions. Therefore, it is natural to start with approximation schemes. Perhaps the simplest among them is quantum field theory in curved spacetimes, where the gravitational field is treated as a classical, passive entity and analyzes the effects of the curved spacetime geometry on quantized matter. At first, this appears to be an oversimplification of the prob- lem. However, this approach led to some key insights in the mid-1970s. The

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 9 most striking among them is the Hawking effect: black holes radiate as though they are blackbodies. This discovery brought together general relativity, quan- tum field theory, and thermodynamics and provided powerful hints for quantum gravity. In particular, it became physically meaningful to assign thermodynamic parameters such as temperature and entropy to black holes in terms of their geometric properties. This posed a concrete challenge to any candidate quantum theory of gravity: Explain the origin of these thermodynamic properties in terms of microscopic degrees of freedom as is done for ideal gases and other everyday systems. As described below, there has been considerable recent progress on this challenge. Over the past decade, quantum field theory in curved spacetimes has evolved considerably, especially through the development of powerful algebraic methods, and has now become a mature branch of mathematical physics. On the physical side, to gain insight into the role of very high frequencies in the Hawking effect, quantum physics around "dumb holes" the acoustic analogs of black holes- has been studied. These model systems also exhibit Hawking radiation (see Box 3.5) and the radiation spectrum turns out to be quite robust, surprisingly insensi- tive to changes in the assumed properties of the extreme high frequency modes. Substantial progress occurred also in another approximation method, that of ef- fective field theories. Here, theorists do treat the gravitational field quantum mechanically, but they focus only on the implications of these quantum effects on length scales large compared to up. Thus, although quantum general relativity is "perturbatively non-renormalizable," theorists can nonetheless extract from it meaningful information to describe physics in the situation where the curvature of spacetime is small compared to that at the Planck scale. This is an interesting development, especially because in the 1970s, such non-renormalizable quantum theories were widely regarded as being devoid of physical content. A number of approaches have been developed to go beyond such approxima- tions. Notable among them are Euclidean quantum gravity, the dynamical trian- gulation method, Regge calculus, asymptotic quantization, reformulation of gen- eral relativity as a dynamical theory of null hyper-surfaces, twister theory, and non-commutative geometry. However, in terms of providing answers to the key questions, two directions stand out: string theory and quantum theory of geom- etry. In both of these approaches, considerable progress has already been made on the first three key questions listed above. String Theory During the past decade, string theory has emerged as a leading candidate for a quantum theory of gravity. In addition, this theory appears to achieve another long-standing goal of theoretical physics: It may provide a unified theory of all known forces and particles. The starting point is remarkably simple. One as- sumes that elementary particles are not point-like, but rather actually different

92 GRAVITATIONS PHYSICS: E~LOHNG THE STRUT OF SPACE^D TIME BOX 3.5 Black Holes and Quantum Physics In the early 1 970s, the properties of black holes were studied and formulated in terms of the laws of black hole mechanics. It was noticed that there was a striking similarity between these laws and the ordinary laws of thermodynamics. The an- alog of the temperature T was a multiple of the surface gravity of the black hole K, which is similar to g on Earth's surface. The analog of the entropy S was a multiple of the area of the event horizon A. More precisely, there were the following corre- spondences: Black Hole Mechanics K iS constant. aM= KDA/8~G. aA 2 0. Thermodynamics Tis constant. aE= 7OS. aside. It was believed at the time that the above relationships were only an analogy, since the defining property of black holes was that nothing can escape their grav- itational pull. In particular, they did not emit the radiation characteristic of an object with non-zero temperature. However, a few years later it was shown that when quantum effects are included, this analogy becomes exact. Because of an analog of the tunneling process in elementary quantum mechanics called the Hawking effect, particles can escape from black holes. Thus, black holes are not really black. They radiate just like hot objects with temperature Tbh = (~/2~c). This implies that black hole entropy is given by Sbh = A14~2p, where Ip is the Planck length. Therefore, in a fundamental statistical mechanical description, a macro- scopic black hole of area A should have eSbh microstates a huge number. It has taken 25 years to obtain a fundamental description of these microstates. In the past few years this fundamental description has finally been achieved in both of the main approaches to quantum gravity. However, important issues still remain, and there should be further exciting developments in this area over the next decade. excitations of a one-dimensional extended object the string. When an ordinary violin string is plucked, it vibrates at certain characteristic frequencies producing the usual notes. Fundamental strings are much smaller (of order up in size), but when they are excited they also vibrate at certain frequencies. Different modes of vibration are seen as electrons, quarks, photons, and so on. This provides a strikingly simple unified picture. The basic interaction between strings is through a simple splitting and join- ing process. Remarkably, the description of this process automatically incorpo- rates the known interactions between the elementary particles. The relation between string theory and general relativity can be seen in two ways. First, one mode of the string describes a graviton (a small fluctuation of the gravitational field), and the classical scattering of strings in this mode reproduces the

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 93 perturbative expansion of general relativity. More importantly, when strings in curved spacetime are studied, a consistency condition on the spacetime geometry emerges which is Einstein's equation of general relativity, augmented by correc- tions that are only important at the Planck scale. In fact, if general relativity were not already known, string theory would predict it as the description of gravity for distances much larger than the size of the string. Until recently, quantum effects in string theory were mostly discussed in the context of perturbation theory. A background spacetime geometry is assumed (satisfying the above consistency condition) and small fluctuations about it are quantized. This is not sufficient to answer the important questions about the big bang or what happens deep inside a black hole. These issues appear to require a complete non-perturbative formulation of string theory which is not yet available. However, in the past few years, a number of non-perturbative facts about the theory have nonetheless been found. This is possible largely because string theory incorporates supersymmetry, a powerful symmetry first discussed in the 1970s. Supersymmetry implies that certain results computed perturbatively are, in fact, exact. String theory has had a number of achievements over the past decade. Here the COP focuses on those achievements that relate directly to gravity and the structure of space and time. The apparently obvious three-dimensional nature of space need not be correct. It is possible that we experience three dimensions because the extra dimensions are curled up into a very small ball. Our measure- ments of space so far might simply be too crude to detect such extra dimensions. In string theory, space and time are no longer fundamental, but instead are de- rived concepts. One early result is that space must have more than three dimen- sions. (The perturbative formulation of string theory predicts nine dimensions, but recent non-perturbative arguments suggest that in the full theory, the number is ten.) T-duality. Suppose one direction in space is curled up into a circle of radius R. In addition to the usual string states, there are now extra states corresponding to strings winding around this circle. The net effect of these extra states is that the spectrum of the string is exactly the same as if the circle had radius 1/R. Further- more, the interactions between string states are also invariant under changing the radius of a circle from R to 1/R. This means that very small circles are indistin- guishable from large circles in string theory. Singularities. As discussed elsewhere in this report, general relativity predicts the existence of places in the universe where the spacetime curvature is infinite. General relativity breaks down at these "singularities." Since string theory modi- fies general relativity even classically, it is important to know whether singu- larities exist in string theory as well. It has been shown that several spacetimes that are singular in general relativity are completely nonsingular when embedded

94 GRAVITATIONS PHYSICS: E~LOHNG THE STRUT OF SPACE^D TIME in string theory. However, it has also been shown that there are some singular solutions even in string theory. These examples are not very physical, and so it is not yet known whether these singularities are likely to arise in nature. Topology Change. The topology of space is a measure of how the space is connected e.g., whether it has holes like the surface of a donut. A long-standing question is whether the topology of space in our universe can change over time. According to general relativity, the answer is no: Topology change always results in singularities. In string theory the situation is different. It has been shown that the topology of space can change in a way that is non-singular in string theory. Quantum Properties of Black Holes. The most important achievement has undoubtedly been the successful description of black hole entropy in terms of quantum string states. As discussed above, this has been a challenge for more than 20 years. For certain large black holes with electric charge near the maxi- mum allowed value, the number of string states with the same charge and mass turns out to be precisely the number predicted from black hole thermodynamics. Even more importantly, the interactions between these states turn out to precisely reproduce the Hawking spectrum of radiation. This is a remarkable achievement. For more general black holes, theorists can identify a class of string states associ- ated with a black hole which scale in the expected way with the mass and charge, but numerical coefficients in the entropy formulas have not yet been checked. Quantum Theory of Geometry In general relativity, spacetime geometry is a dynamical entity that interacts with matter and has degrees of freedom of its own. Therefore, to unify the principles of general relativity and quantum theory, it is natural to take this physical role of geometry to be fundamental and probe its quantum nature from first principles. Over the past decade, a detailed theory has been developed starting from this viewpoint which in turn has provided some key insights on the nature of quantum gravity effects. This approach is "non-perturbative" in the sense that a classical spacetime is not the starting point to which quantum fluctuations to its geometry are then added. There is no background spacetime; everything, including geometry, is dynamical and quantum mechanical. Indeed, the strategy is just the opposite of that followed in perturbative treatments: Rather than starting with quantum matter on classical spacetimes, one first quantizes geometry and then incorpo- rates matter. This procedure is motivated by two considerations. The first comes from general relativity in which some of the simplest and yet most interesting physical systems black holes and gravitational waves consist of "pure geom- etry." The second comes from quantum theory where the occurrence of infinities

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 95 at short distances suggests that it may be physically incorrect to quantize matter assuming that spacetime can be regarded as a smooth continuum at arbitrarily small scales. The detailed implementation of these ideas requires a new mathematical and conceptual framework, since the standard methods used in quantum theories of non-gravitational forces are tied to the availability of a background spacetime that is now absent. An important recent advance was the systematic construction of the appropriate substitutes. The resulting mathematical framework is now sufficiently rigorous to ensure that there are no hidden infinities or other internal . . . Inconsistencies. The key results obtained from this framework can be summarized as follows. Fundamental Discreteness. Over the past 5 years, this approach has led to a detailed quantum theory of geometry. The framework shares several basic con- cepts with gauge theories, thereby bringing gravity closer to other fundamental forces. In particular, the fundamental excitations of geometry are coded in the gravitational Wilson loops. They are one-dimensional so that quantum geometry resembles a polymer. However, when densely packed in appropriate configura- tions, these excitations can approximate the three-dimensional spatial continuum. Quantum analogs of observable geometrical quantities such as areas of surfaces and volumes of regions called geometric operators are well-defined. They have the striking property that their values are quantized, that is, can change only in discrete steps. Thus, at the Planck scale, the continuum picture breaks down and geometry becomes "polymer-like." Several properties of the geometric operators have been worked out. For instance, the allowed discrete values of area crowd rapidly as area increases; the difference between them, called the level spacing, goes to zero exponentially quickly, making the continuum picture an excellent approximation in laboratory physics. However, since the Planck length up is so small, can such details ever bear on the macroscopic world? What if, for example, the level spacing were uniform, like that in a harmonic oscillator, with steps of the order of {p? Could such alternatives be physically distinguished? Surprisingly, using quantum field theory in black hole spacetimes, one can. While the actual level spacing of area is consistent with the blackbody spectrum of the Hawking effect, the uniform level spacing is not. Thus, there are checks on predictions. Black Hole Thermodynamics. Since a black hole in general relativity is "pure geometry," it is natural to use quantum geometry to unravel its microscopic degrees of freedom. Recently, this task was carried out for nonrotating black holes, possibly with charges. For large black holes, the number of microstates grows exponentially with area, showing that the entropy is proportional to area. From this perspective, the mechanism underlying black hole evaporation is strik- ingly simple: Quanta of area are converted to quanta of matter. This ongoing

96 GRAVITATIONS PHYSICS: E~LOHNG THE STRUCTURE OF SPACE ED TIME work provides a quantum mechanical manifestation of the idea that geometry is a physical entity. Quantum Dynamics. Quantum geometry provides a mathematical language to formulate a wide variety of quantum gravity theories, just as differential geom- etry does in the case of classical gravity. However, so far quantum dynamics has been explored only in general relativity, possibly coupled to matter, and super- gravity, the extension of general relativity which incorporates supersymmetry. The central question is, Can these quantum theories admit an exact, mathemati- cally consistent formulation even though they are "perturbatively nonrenormal- izable?" In two (rather than three) space dimensions, the answer is in the affirma- tive even with certain types of matter. Although this lower-dimensional theory is not of direct physical interest, it faces most of the conceptual difficulties of the three-dimensional theory, and the application of perturbative methods had led to a general belief that a consistent quantum theory would not exist. Not only does a satisfactory theory exist but the non-perturbative formulation also provides useful hints for higher-dimensional theories. Over the last 3 years, there has also been considerable work in four dimen- sions which has provided an example of how quantum Einstein equations can be formulated rigorously. This is an interesting development in mathematical phys- ics. However, it is not yet clear whether this formulation can successfully answer those physical questions that are motivated by semi-classical considerations. Another approach to quantum dynamics leads to an unexpected interplay with a branch of topology, namely, the theory of knots. In particular, some of the well- known "knot invariants" automatically solve quantum Einstein equations, and there are indications of deeper relations between quantum general relativity and knot theory. Opportunities The coming decade is likely to see substantial further progress in quantum gravity. With an eye toward the key questions listed above, the COP briefly describes some of the opportunities that await us. The pace of progress in string theory has been extremely rapid during the past few years. Indeed, within the past year, a proposal for a non-perturbative formulation of the theory has been made, which is applicable when the cosmo- logical constant is negative. While this is not believed to be the case in nature, this formulation can still be used as a model to study quantum gravitational processes such as the evaporation of black holes. This proposal incorporates a novel "holographic" view of space and time, in which our usual notions of local- ity and causality hold only approximately. Much effort will be devoted in com- ing years to establish in detail that this proposal is correct and to extend it in such

ACHIEVEMENTS AND OPPORTUNITIES IN GRAVITATIONAL PHYSICS 97 a way that the cosmological constant need not be specified a priori. If these steps can be completed, we may finally have a workable quantum theory of gravity. Significant advances are also expected in the approach based on quantum geometry. In this framework, quantum dynamics was initially discussed using Hamiltonian methods. Spacetime formulations of the required theory are now being pursued vigorously in which quantum geometry serves to unify results from apparently three distinct areas of research, pursued independently by rela- tivists, quantum field theorists, and mathematicians. These methods provide a new avenue to formulate and discuss quantum Einstein equations and are better suited for semi-classical considerations. Physical ramifications of the quantum nature of geometry will also be explored further. In particular, it is likely that quantum field theories on quantum geometries will be studied. Since the funda- mental geometric excitations are one-dimensional, the effective spacetime di- mension is now reduced. The key question then is whether this feature will free quantum theories of non-gravitational interactions from the usual short-distance infinities. If so, the old and cherished hope that quantum gravity may cure quantum field theories will be realized. So far, string theory has been developed largely by high-energy theorists and quantum geometry by relativists. This is reflected in the choice of issues that are emphasized in the two approaches. However, there are tantalizing similarities such as the importance of one-dimensional objects. Furthermore, as the results on black hole thermodynamics indicate, both approaches are now addressing the same physical problems. Their strengths are complementary. One enables quan- tum physics to be done without a background spacetime but provides no guidance on how various physical fields couple to gravity and to one another. The other has an in-built powerful principle that dictates all couplings but has yet to com- pletely free itself from reliance on a background geometry. Much progress would occur if there were more interaction between the two communities. It is clear that recent results on the quantum properties of black holes will be extended using both string theory and quantum geometry. In this area, there are several exciting challenges. The two approaches have led to rather different physical pictures of a quantum black hole, one based on extended objects in higher-dimensional spacetimes, and the other, on the polymer-like excitations of geometry of ordinary space. Are these two pictures "complementary" in a suit- able sense? More generally, what is the relation between them? Another chal- lenge is to derive the laws of black hole thermodynamics from quantum gravity, in full generality, allowing for departures from thermal equilibrium. An even more important open question is whether information thrown into a black hole is lost forever, or is ultimately recovered in the evaporation process. If it is indeed lost forever, as suggested by the original semi-classical calculations in the 1970s, then some of the basic principles of quantum theory would have to be modified. However, the recent string calculations indicate that information is not lost. It is

98 GRAVITATIONAL PHYSICS: EXPLORING THE STRUCTURE OF SPACE AND TIME possible that this long-standing "black hole information puzzle" will be resolved in the near future. Considerable progress can also be expected in applying these developing theories of quantum gravity to cosmology. Indeed it could be argued that while most effects of quantum gravity are not observable, the effects of the quantum fluctuations in geometry and matter near the big bang are all around us. We see them in anisotropies in the cosmic background radiation and in the large-scale distributions of galaxies. The objective of quantum cosmology is to understand the earliest moments after the big bang. Quantum gravity is central to this task, and cosmology is one of quantum gravity's most important applications. (These issues are further discussed in Section III of this chapter.) It is quite possible that qualitatively new and unexpected effects will be discovered in the coming years, the quantum gravity analogs of E = mc2 of special relativity. For example, it was recently found that in the two- and three- dimensional exactly soluble models, unexpectedly large quantum fluctuations can arise in the spacetime geometry because the coupling between general rela- tivistic gravity and matter can magnify small quantum uncertainties in matter sources of gravitation into huge uncertainties in the gravitational field. In the coming years, these results are likely to be extended to four dimensions and may then have experimental consequences. Similarly, there are directions in which the current ideas in string theory could be confronted with experiments. For example, discovery of supersymmetry in particle accelerators would lend support to an important ingredient of string theory. A second example arises from the fact that one mode of the string, the dilator, has interactions like gravity but couples to matter in a different way. (See Section IV of this chapter.) This might produce violations of the equivalence principle at a detectable level. More direct tests may also be possible in spite of the fact that the energy scale of quantum gravity is very high, 10~9 GeV. In the 1980s, for example, experiments were performed to directly test the predictions of grand unified theories on proton decay. The processes responsible for this phenomenon are only a few orders of magnitude below the quantum gravity scale. Yet, it was possible to test these theories without having to accelerate particles to such high energies; the experiments involved confining a very large number of protons and waiting sufficiently long to see if any of them decayed. In the same spirit ~ ~ ~ .# .# , attempts have recently been made to put limits on certain quantum gravity effects using observations of TeV gamma-ray flares. The idea is that the tiny effects on the propagation of gamma-rays due to the Planck-scale fluctuations in the spacetime geometry can accumulate during their long flight over cosmological distances and lead to an observable dispersion. It is likely that these ideas will be refined over the next decade and enable researchers to experimentally distinguish between possible quantum gravity scenarios.

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Gravitational Physics assesses the achievements of the field over the past decade in both theory and experiment, identifies the most promising opportunities for research in the next decade, and describes the resources necessary to realize those opportunities. A major theme running through the opportunities is the exploration of strong gravitational fields, such as those associated with black holes.

The book, part of the ongoing decadal survey Physics in a New Era, examines topics such as gravitational waves and their detection, classical and quantum theory of strong gravitational fields, precision measurements, and astronomical observations relevant to the predictions of Einstein's theory of general relativity.

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