Constructing black hole entropy from gravitational collapse

TL;DR

This paper links the increase in gravitational entropy during collapse to the surface area change of the collapsing body, providing a new perspective on black hole entropy from gravitational collapse.

Contribution

It introduces a method to derive black hole entropy from gravitational entropy changes during collapse using the covariant 1+1+2 formalism.

Findings

Gravitational entropy outside the collapsing body increases with surface area.

Black hole entropy relates to the variation of vacuum gravitational entropy.

The approach applies to Oppenheimer-Snyder-Datt collapse models.

Abstract

Based on a recent proposal for the gravitational entropy of free gravitational fields, we investigate the thermodynamic properties of black hole formation through gravitational collapse in the framework of the semitetrad 1+1+2 covariant formalism. In the simplest case of an Oppenheimer-Snyder-Datt collapse we prove that the change in gravitational entropy outside a collapsing body is related to the variation of the surface area of the body itself, even before the formation of horizons. As a result, we are able to relate the Bekenstein-Hawking entropy of the black hole endstate to the variation of the vacuum gravitational entropy outside the collapsing body.