Instability of sphaleron black holes in asymptotically anti-de Sitter space-time

TL;DR

This paper proves that sphaleron black holes in a specific Einstein-Yang-Mills-Higgs theory with anti-de Sitter boundary conditions are inherently unstable, highlighting their limitations in such spacetime configurations.

Contribution

It provides a rigorous proof of the instability of sphaleron black holes in asymptotically anti-de Sitter space within a particular gauge theory.

Findings

Sphaleron black holes are unstable in this setting.

The instability is proven mathematically.

Implications for the stability of similar solutions.

Abstract

We prove that sphaleron black holes in ${\mathfrak {su}}(2)$ Einstein-Yang-Mills-Higgs theory with a Higgs doublet in four-dimensional, asymptotically anti-de Sitter space-time are unstable.