The evolution of unstable black holes in anti-de Sitter space

TL;DR

This paper investigates the stability of large black holes in anti-de Sitter space, showing that thermodynamic instability correlates with dynamical instability and discussing implications for cosmic censorship.

Contribution

It provides numerical evidence linking thermodynamic and dynamical stability of black holes in anti-de Sitter space, challenging no-hair theorems and discussing potential cosmic censorship violations.

Findings

Unstable black holes lack local thermodynamic stability.

Thermodynamic and dynamical instabilities are correlated.

No-hair theorems do not hold in anti-de Sitter space.

Abstract

We examine the thermodynamic stability of large black holes in four-dimensional anti-de Sitter space, and we demonstrate numerically that black holes which lack local thermodynamic stability often also lack stability against small perturbations. This shows that no-hair theorems do not apply in anti-de Sitter space. A heuristic argument, based on thermodynamics only, suggests that if there are any violations of Cosmic Censorship in the evolution of unstable black holes in anti-de Sitter space, they are beyond the reach of a perturbative analysis.