Statistical black-hole thermodynamics
Traditional methods from statistical thermodynamics, with appropriate modifications, are used to study several problems in black-hole thermodynamics. 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 (it is found to agree with what would be expected from Hawking's results) 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. We also formulate a Jaynes-type maximum-uncertainty principle for black holes, and apply it to obtain the probability distribution among Kerr solution states for an isolated radiating Kerr hole. (AIP)
- Research Organization:
- Department of Physics, Ben Gurion University of the Negev, Beer Sheva 84120, Israel
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-33-021009
- OSTI ID:
- 4086193
- Journal Information:
- Phys. Rev., D, v. 12, no. 10, pp. 3077-3085, Other Information: Orig. Receipt Date: 30-JUN-76
- Country of Publication:
- United States
- Language:
- English
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