Gravitational entropy of nonstationary black holes and spherical shells

William A. Hiscock
Phys. Rev. D 40, 1336 – Published 15 August 1989
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Abstract

The problem of defining the gravitational entropy of a nonstationary black hole is considered in a simple model consisting of a spherical shell which collapses into a preexisting black hole. The second law of black-hole mechanics strongly suggests identifying one-quarter of the area of the event horizon as the gravitational entropy of the system. It is, however, impossible to accurately locate the position of the global event horizon using only local measurements. In order to maintain a local thermodynamics, it is suggested that the entropy of the black hole be identified with one-quarter the area of the apparent horizon. The difference between the event-horizon entropy (to the extent it can be determined) and the apparent-horizon entropy may then be interpreted as the gravitational entropy of the collapsing shell. The total (event-horizon) gravitational entropy evolves in a smooth (C0) fashion, even in the presence of δ-functional shells of matter.

  • Received 17 April 1989

DOI:https://doi.org/10.1103/PhysRevD.40.1336

©1989 American Physical Society

Authors & Affiliations

William A. Hiscock

  • Department of Physics, Montana State University, Bozeman, Montana 59717

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Issue

Vol. 40, Iss. 4 — 15 August 1989

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