An Operational Approach To Black Hole Entropy

Details An Operational Approach To Black Hole Entropy An Operational Approach To Black Hole Entropy

1997-12-22

arxiv.org/abs/gr-qc/9712085v1

Phys.Rev. D57 (1998) 6311-6316

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, LaTeX, submitted to Phys. Rev. D

Scientific paper

10.1103/PhysRevD.57.6311

In this paper we calculate the entropy of a thin spherical shell that contracts reversibly from infinity down to its event horizon. We find that, for a broad class of equations of state, the entropy of a non-extremal shell is one-quarter of its area in the black hole limit. The considerations in this paper suggest the following operational definition for the entropy of a black hole: $S_{BH}$ is the equilibrium thermodynamic entropy that would be stored in the material which gathers to form the black hole, if all of this material were compressed into a thin layer near its gravitational radius. Since the entropy for a given mass and area is maximized for thermal equilibrium we expect that this is the maximum entropy that could be stored in the material before it crosses the horizon. In the case of an extremal black hole the shell model does not assign an unambiguous value to the entropy.

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