On the stability of dyons and dyonic black holes in Einstein-Yang-Mills theory

TL;DR

This paper proves the existence of stable dyonic soliton and black hole solutions in Einstein-Yang-Mills theory in anti-de Sitter space, showing stability under linear spherically symmetric perturbations near trivial solutions.

Contribution

It demonstrates the existence and linear stability of non-trivial dyonic solutions in Einstein-Yang-Mills theory in anti-de Sitter space, expanding understanding of their stability properties.

Findings

Existence of stable dyonic soliton solutions.

Existence of stable dyonic black hole solutions.

Stability proven under linear, spherically symmetric perturbations.

Abstract

We investigate the stability of four-dimensional dyonic soliton and black hole solutions of ${\mathfrak {su}}(2)$ Einstein-Yang-Mills theory in anti-de Sitter space. We prove that, in a neighbourhood of the embedded trivial (Schwarzschild-)anti-de Sitter solution, there exist non-trivial dyonic soliton and black hole solutions of the field equations which are stable under linear, spherically symmetric, perturbations of the metric and non-Abelian gauge field.