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

TL;DR

This paper demonstrates that certain black holes and solitons with Yang-Mills hair in anti-de Sitter space are stable under odd-parity, non-spherical linear perturbations, extending previous stability results.

Contribution

It introduces a curvature-based perturbation formalism and applies it to establish stability of hairy black holes and solitons in AdS space under odd-parity perturbations.

Findings

Solutions stable under spherically symmetric perturbations remain stable under odd-parity perturbations.

The perturbation formalism effectively analyzes stability using curvature quantities.

Stability results support the robustness of hairy black holes in AdS space.

Abstract

Using a recently developed perturbation formalism based on curvature quantities, we investigate 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 odd-parity, linear, non-spherically symmetric perturbations.