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

Understand

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.