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

Abstract

We investigate the stability of four-dimensional dyonic soliton and black hole solutions of 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.