Mathematics – Probability
Scientific paper
Nov 1975
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975phrvd..12.3077b&link_type=abstract
Physical Review D - Particles and Fields, 3rd Series, vol. 12, Nov. 15, 1975, p. 3077-3085. Research supported by the Israel Aca
Mathematics
Probability
105
Black Holes (Astronomy), Entropy, Probability Distribution Functions, Statistical Analysis, Thermodynamics, Astronomical Models, Black Body Radiation, Maximum Principle, Spontaneous Emission, Thermodynamic Equilibrium
Scientific paper
Jaynes's maximum-uncertainty method for computing probabilities is used to show that the earlier-formulated generalized second law is respected in statistically averaged form in the process of spontaneous radiation by a Kerr black hole discovered by Hawking, and also in the case of a Schwarzschild hole immersed in a bath of black-body radiation, however cold. The generalized second law is used to motivate a maximum-entropy principle for determining the equilibrium probability distribution for a system containing a black hole. As an application we derive the distribution for the radiation in equilibrium with a Kerr hole and the form of the associated distribution among Kerr black-hole solution states of definite mass. The same results are shown to follow from a statistical interpretation of the concept of black-hole entropy as the natural logarithm of the number of possible interior configurations that are compatible with the given exterior black-hole state.
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