Black hole dynamics from thermodynamics in Anti-de Sitter space

TL;DR

This paper explores the connection between thermodynamic and dynamical instabilities of large black holes in Anti-de Sitter space, showing that thermodynamic instability predicts dynamical instability through linear perturbation analysis.

Contribution

It demonstrates that all linear metric perturbations leading to thermodynamic instability also cause dynamical instability, linking thermodynamics to black hole stability in AdS space.

Findings

Thermodynamically unstable black holes are dynamically unstable.

Linear perturbations suppressing metric fluctuations induce instability.

Dynamical instability can be explained by the Second Law of Thermodynamics.

Abstract

We work on the relation between the local thermodynamic instability and the dynamical instability of large black holes in four-dimensional anti-de Sitter space proposed by Gubser and Mitra. We find that all perturbations suppressing the metric fluctuations at linear order become dynamically unstable when black holes lose the local thermodynamic stability. We discuss how dynamical instabilities can be explained by the Second Law of Thermodynamics.