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

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