Dynamic and Thermodynamic Stability and Negative Modes in Schwarzschild-Anti-de Sitter

TL;DR

This paper investigates the stability and negative modes of Schwarzschild-anti-de Sitter black holes within finite cavities, establishing links between thermodynamic stability and classical solution stability, and supporting the positive energy conjecture.

Contribution

It demonstrates the correspondence between negative modes and thermodynamic stability for Schwarzschild-AdS black holes, extending the analysis to the infinite cavity limit and providing evidence for the positive energy conjecture.

Findings

Non-existence of negative modes correlates with thermodynamic stability.

Infinite cavity limit allows a well-defined stability analysis.

Supports the positive energy conjecture by Horowitz and Myers.

Abstract

The thermodynamic properties of Schwarzschild-anti-de Sitter black holes confined within finite isothermal cavities are examined. In contrast to the Schwarzschild case, the infinite cavity limit may be taken which, if suitably stated, remains double valued. This allows the correspondence between non-existence of negative modes for classical solutions and local thermodynamic stability of the equilibrium configuration of such solutions to be shown in a well defined manner. This is not possible in the asymptotically flat case. Furthermore, the non-existence of negative modes for the larger black hole solution in Schwarzschild-anti-de Sitter provides strong evidence in favour of the recent positive energy conjecture by Horowitz and Myers.