An Operational Approach To Black Hole Entropy

TL;DR

This paper proposes an operational method to define black hole entropy by analyzing the entropy of a contracting thin shell, showing it approaches one-quarter of its area in the black hole limit, thus linking thermodynamics with gravitational collapse.

Contribution

It introduces a shell-based operational definition of black hole entropy applicable to non-extremal black holes, connecting entropy with material compression near the horizon.

Findings

Entropy of a contracting shell approaches one-quarter of its area.

The proposed definition aligns with the Bekenstein-Hawking entropy for non-extremal black holes.

Extremal black holes do not have a clear entropy value in this model.

Abstract

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.