On the linear stability of solitons and hairy black holes with a negative cosmological constant: the even-parity sector

TL;DR

This paper demonstrates the linear stability of certain black holes and solitons with Yang-Mills hair in anti-de Sitter space under even-parity, non-spherical perturbations, confirming their robustness.

Contribution

It completes the stability analysis by showing that solutions stable under spherically symmetric perturbations remain stable under more general even-parity perturbations.

Findings

Stable solutions have no linear instabilities under even-parity perturbations.

Established the existence of stable hairy black holes and solitons with AdS asymptotics.

Extended previous stability results to include non-spherical perturbations.

Abstract

Using a recently developed perturbation formalism based on curvature quantities, we complete our investigation of the linear stability of black holes and solitons with Yang-Mills hair and a negative cosmological constant. We show that those solutions which have no linear instabilities under odd- and even-parity spherically symmetric perturbations remain stable under even-parity, linear, non-spherically symmetric perturbations. Together with the result from a previous work, we have therefore established the existence of stable hairy black holes and solitons with anti-de Sitter asymptotic.