Constructing black hole entropy from gravitational collapse

TL;DR

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

Contribution

It introduces a novel approach connecting gravitational entropy to surface area changes during collapse, extending the understanding of black hole thermodynamics.

Findings

Gravitational entropy outside collapsing bodies increases with surface area.

Black hole entropy relates to vacuum gravitational entropy variation.

Entropy change occurs before horizon formation.

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.