Statistical black-hole thermodynamics

Phys. Rev. D 12, 3077 – Published 15 November 1975
Jacob D. Bekenstein

Abstract

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.

DOI: http://dx.doi.org/10.1103/PhysRevD.12.3077

  • Received 12 May 1975
  • Published in the issue dated 15 November 1975

© 1975 The American Physical Society

Authors & Affiliations

Jacob D. Bekenstein

  • Department of Physics, Ben Gurion University of the Negev, Beer Sheva 84120, Israel

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