Thermodynamics of a black hole in a cavity

TL;DR

This paper provides a unified thermodynamic analysis of self-gravitating radiation and black holes in a cavity, examining stability, fluctuations, and the effects of angular momentum on black hole evaporation.

Contribution

It introduces a comprehensive thermodynamic framework for black holes in a cavity, including fluctuation analysis and the impact of angular momentum on stability and evaporation.

Findings

Transitions from metastable to stable states are exponentially unlikely.

Metastable states persist until near the critical point where no metastability remains.

High angular momentum causes black holes to lose most of their mass before evaporation.

Abstract

We present a unified thermodynamical description of the configurations consisting on self-gravitating radiation with or without a black hole. We compute the thermal fluctuations and evaluate where will they induce a transition from metastable configurations towards stable ones. We show that the probability of finding such a transition is exponentially small. This indicates that, in a sequence of quasi equilibrium configurations, the system will remain in the metastable states till it approaches very closely the critical point beyond which no metastable configuration exists. Near that point, we relate the divergence of the local temperature fluctuations to the approach of the instability of the whole system, thereby generalizing the usual fluctuations analysis in the cases where long range forces are present. When angular momentum is added to the cavity, the above picture is slightly modified. Nevertheless, at high angular momentum, the black hole loses most of its mass before it reaches the critical point at which it evaporates completely.