Entropy of quasiblack holes

TL;DR

This paper investigates the origin of black hole entropy by examining quasiblack holes, showing that their surface properties lead to the Bekenstein-Hawking entropy in the nonextremal case, and discussing extremal cases.

Contribution

It demonstrates that the entropy of quasiblack holes approaches the Bekenstein-Hawking value through surface stresses, providing insights into black hole entropy's universality and origin.

Findings

Entropy approaches A/4 in the quasihorizon limit for nonextremal cases.

Surface stresses on the quasihorizon determine the entropy.

Universal entropy value independent of internal matter distribution.

Abstract

We trace the origin of the black hole entropy S replacing a black hole by a quasiblack hole. Let the boundary of a static body approach its own gravitational radius, in such a way that a quasihorizon forms. We show that if the body is thermal with the temperature taking the Hawking value at the quasihorizon limit, it follows, in the nonextremal case, from the first law of thermodynamics that the entropy approaches the Bekenstein-Hawking value S=A/4. In this setup, the key role is played by the surface stresses on the quasihorizon and one finds that the entropy comes from the quasihorizon surface. Any distribution of matter inside the surface leads to the same universal value for the entropy in the quasihorizon limit. This can be of some help in the understanding of black hole entropy. Other similarities between black holes and quasiblack holes, such as the mass formulas for both objects had been found previously. We also discuss the entropy for extremal quasiblack holes, a more subtle issue.