Topological Black Holes of Gauss-Bonnet-Yang-Mills Gravity

We present the asymptotically AdS solutions of Gauss-Bonnet gravity with hyperbolic horizon in the presence of a non-Abelian Yang-Mills field with the gauge semisimple group $So(n(n-1)\mathrm{/}2-1,1)$. We investigate the properties of these solutions and find that the non-negative mass solutions in 6 and higher dimensions are real everywhere with spacelike singularities. They present black holes with one horizon and have the same causal structure as the Schwarzschild spacetime. The solutions in 5 dimensions or the solutions in higher dimensions with negative mass are not real everywhere. In these cases, one needs a transformation to make the solutions real. These solutions may present a naked singularity, an extreme black hole, a black hole with two horizons, or a black hole with one horizon.