Questions of Stability near Black Hole Critical Points

TL;DR

This paper examines how thermal fluctuations influence the stability of charged black holes near critical points, using a novel approach based on the black hole area spectrum and ensemble distinctions.

Contribution

It introduces a new method analyzing black hole stability near critical points by incorporating thermal fluctuations and the black hole area spectrum.

Findings

Thermal fluctuations affect black hole stability near critical points.

Distinction between fixed and fluctuating charge systems impacts stability analysis.

Analysis includes phase transitions like Hawking-Page and extremal limits.

Abstract

In this letter, we discuss how thermal fluctuations can effect the stability of (generally) charged black holes when close to certain critical points. Our novel treatment utilizes the black hole area spectrum (which is, for definiteness, taken to be evenly spaced) and makes an important distinction between fixed and fluctuating charge systems (with these being modeled, respectively, as a canonical and grand canonical ensemble.) The discussion begins with a summary of a recent technical paper [gr-qc/0305018]. We then go on to consider the issue of stability when the system approaches the critical points of interest. These include the $d$-dimensional analogue of the Hawking-Page phase transition, a phase transition that is relevant to Reissner-Nordstrom black holes and various extremal-limiting cases.