Time Evolution of Entropy in Gravitational Collapse

TL;DR

This paper investigates the time evolution of entropy during gravitational collapse, showing that the entropy of a collapsing domain wall stabilizes at a value comparable to the Bekenstein-Hawking entropy after a certain time.

Contribution

It provides a detailed analysis of entropy evolution in gravitational collapse from an asymptotic observer's perspective, highlighting the entropy's approach to a constant value.

Findings

Entropy of the collapsing domain wall becomes constant after a certain time.

The stabilized entropy is of the same order as the Bekenstein-Hawking entropy.

The study offers insights into black hole entropy formation during collapse.

Abstract

We study the time evolution of the entropy of a collapsing spherical domain wall, from the point of view of an asymptotic observer, by investigating the entropy of the entire system (i.e. domain wall and radiation) and induced radiation alone during the collapse. By taking the difference, we find the entropy of the collapsing domain wall, since this is the object which will form a black hole. We find that for large values of time (times larger than $t/R_s\approx8$), the entropy of the collapsing domain wall is a constant, which is of the same order as the Bekenstein-Hawking entropy.