Time Evolution of Temperature and Entropy of a Gravitationally Collapsing Cylinder

TL;DR

This paper studies the time evolution of temperature and entropy during gravitational collapse of a cylindrical domain wall, revealing that entropy approaches a constant near Hawking entropy but decreases over time, preventing spontaneous collapse.

Contribution

It extends previous spherical collapse models to a cylindrical topology using a (3+1) BTZ metric, analyzing radiation spectrum and thermodynamics during collapse.

Findings

Spectrum is quasi-thermal with increasing thermality near the horizon.

Late-time temperature closely matches Hawking temperature.

Entropy approaches a constant close to Hawking entropy but decreases over time.

Abstract

We investigate the time evolution of the temperature and entropy of a gravitationally collapsing cylinder, represented by an infinitely thin domain wall, as seen by an asymptotic observer. Previous work has shown that the entropy of a spherically symmetric collapsing domain approaches a constant, and we follow this procedure using a (3+1) BTZ metric to see if a different topology will yield different results. We do this by coupling a scalar field to the background of the domain wall and analyzing the spectrum of radiation as a function of time. We find that the spectrum is quasi-thermal, with the degree of thermality increasing as the domain wall approaches the horizon. The thermal distribution allows for the determination of the temperature as a function of time, and we find that the late time temperature is very close to the Hawking temperature and that it also exhibits the proper scaling with the mass. From the temperature we find the entropy. Since the collapsing domain wall is what forms a black hole, we can compare the results to those of the standard entropy-area relation. We find that the entropy does in fact approach a constant that is close to the Hawking entropy. However, the time dependence of the entropy shows that the entropy decreases with time, indicating that a (3+1) BTZ domain wall will not collapse spontaneously.