The covariant entropy bound in gravitational collapse

TL;DR

This paper investigates the covariant entropy bound during gravitational collapse, demonstrating through an exact model that the entropy crossing the horizon does not exceed the bound, thus confirming its validity in such scenarios.

Contribution

It provides an exact model analysis of gravitational collapse showing the covariant entropy bound holds, addressing previous heuristic arguments.

Findings

Entropy crossing the horizon is within the bound.

The covariant entropy bound is validated during collapse.

The model confirms the bound's applicability in realistic collapse scenarios.

Abstract

We study the covariant entropy bound in the context of gravitational collapse. First, we discuss critically the heuristic arguments advanced by Bousso. Then we solve the problem through an exact model: a Tolman-Bondi dust shell collapsing into a Schwarzschild black hole. After the collapse, a new black hole with a larger mass is formed. The horizon, $L$, of the old black hole then terminates at the singularity. We show that the entropy crossing $L$ does not exceed a quarter of the area of the old horizon. Therefore, the covariant entropy bound is satisfied in this process.