Gravitation, Cosmology, and Cosmic-Ray Physics (1986) / Chapter Skim
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8. Gravitational Theory: Highlights
8. Gravitational Theory: Highlights
Pages 61-71
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From page 61... ...
The discovery of the binary radio pulsar PSR 1913 + 16 has provided an impressive example of relativistic ejects in its orbital motion (see earlier sections on Perihelion Advance, Einstein's Only Handle in Chapter 2 and on Binary Pulsar in Chapter 5~. However, it has been difficult to discover direct evidence for general relativistic effects in observations of neutron stars themselves.
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From page 62... ...
GRAVITATIONAL COLLAPSE AND BLACK HOLES There is a maximum mass limit for neutron stars. The exact limit depends on the equation of state for nuclear matter, which is not well known.
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From page 63... ...
A black hole may be born in a more or less excited state, depending on the degree of disorder in the gravitational collapse of its progenitor star, but it quickly relaxes to a stationary state by the emission of gravitational waves. The stationary states of black holes are remarkably simple, according to the uniqueness theorems, which state that a stationary black hole must belong to the three-parameter family of black-hole solutions of the Einstein equations, the SchwarzschildKerr-Newman solutions.
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From page 64... ...
The area theorem states that, in classical physics, the surface area of a black hole never decreases; this theorem is known as the second law of black-hole dynamics from its parallelism to the Second Law of Thermodynamics, which asserts that entropy never decreases for an isolated system. Small disturbances of stationary black holes, for instance due to small particles falling in or to impinging electromagnetic or gravitational waves, can be worked out in linear perturbation theory.
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From page 65... ...
EXACT SOLUTIONS OF THE EINSTEIN EQUATIONS The Einstein equations are a nonlinear set of coupled partial differential equations, and their complete solution is unknown. The discovery of exact particular solutions has played an important role in the progress of relativity; for instance, the Kerr solution, which is now known to be the unique solution for a rotating, uncharged, stationary black hole, was first found in a systematic search for certain exact solutions known as algebraically special.
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From page 66... ...
However, the nonlinearities in the Einstein equations make the study of — 7 infinity a subtle one. In a general, asymptotically flat space-time in which gravitational waves are propagating toward infinity, the Riemann curvature tensor falls off only as 1/r in the directions (called null infinity)
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From page 67... ...
EMISSION OF GRAVITATIONAL RADIATION Inspired by experiments to detect gravitational radiation, investigators have studied many source models. The calculations carried out include perturbation studies of gravitational collapse and black holes, approximate models of collapsing cores and of colliding neutron stars, and full-scale numerical calculations of gravitational collapse, colliding neutron stars, and colliding black holes (see Figure 8.11.
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From page 68... ...
THE POSITIVE ENERGY THEOREM Gravitational binding energy is negative, because gravity is an attractive force. When a body of given mass becomes so compact that the effects of general relativity become significant for its structure, the binding energy becomes comparable with the total rest energy of the matter making up the body.
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From page 69... ...
When this formal argument is made concrete, it indeed yields a rigorous proof of positive energy in general relativity. QUANTUM FIELD THEORY IN CURVED SPACE-TIME The discovery of the Hawking process by which black holes radiate particles quantum mechanically led to extensive development of the theory of quantum-matter fields in curved background space-time.
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From page 70... ...
The gravitational measure in the path integral, the existence of trace anomalies for the stress tensor, and solutions describing topological nontrivial configurations are just some examples. More recently, non-Abelian anomalies and the quantum breaking of coordinate invariance provide other striking illustrations involving gravity, gauge theories, and recent mathematics.
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From page 71... ...
Goals, techniques, and to some extent people are now shared between the cutting edges of these two areas. Supergravity, induced gravity, higher derivative Lagrangians, twistor theory, geometric quantization, discrete gravity, Kaluza-Klein theories, and string and superstring theories are just some of the headings under which new theories of quantum gravity might be grouped.
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