Existence of topological hairy dyons and dyonic black holes in anti-de Sitter SU(N) Einstein-Yang-Mills theory

Abstract

We investigate dyonic black hole and dyon solutions of four-dimensional $SU(N)$ Einstein-Yang-Mills theory with a negative cosmological constant. We derive a set of field equations in this case, and prove the existence of non-trivial solutions to these equations for any integer $N$, with $2N-2$ gauge degrees of freedom. We do this by showing that solutions exist locally at infinity, and at the event horizon for black holes and the origin for solitons. We then prove that we can patch these solutions together regularly into global solutions that can be integrated arbitrarily far into the asymptotic regime. Our main result is to show that dyonic solutions exist in open sets in the parameter space, and hence that we can find non-trivial dyonic solutions in a number of regimes whose magnetic gauge fields have no zeroes, which is likely important to the stability of the solutions.

48 pages

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Cited by in corpus (9)

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• Black holes with $\mathfrak{su}(N)$ gauge field hair and superconducting horizons
• Analytic meronic black holes, gravitating solitons and higher spins in the Einstein $SU(N)$-Yang-Mills theory
• On the global existence of spherically symmetric hairy black holes and solitons in anti-de Sitter Einstein-Yang-Mills theories with compact semisimple gauge groups
• On the existence of topological dyons and dyonic black holes in anti-de Sitter Einstein-Yang-Mills theories with compact semisimple gauge groups
• Non-Abelian clouds around Reissner-Nordström black holes: the existence line
• Dyonic black holes in $\mathfrak{su}(\infty )$ anti-de Sitter Einstein-Yang-Mills theory, characterised by an infinite set of global charges