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

TL;DR

This paper explores new asymptotically AdS black hole solutions in Gauss-Bonnet gravity coupled with a non-Abelian Yang-Mills field, analyzing their properties and causal structures across different dimensions.

Contribution

It introduces novel solutions of Gauss-Bonnet-Yang-Mills gravity with hyperbolic horizons and examines their physical characteristics and singularity structures.

Findings

Non-negative mass solutions in 6+ dimensions are real with spacelike singularities.

Solutions in 5 dimensions or with negative mass may require transformations to be real.

Various horizon structures including naked singularities and multiple horizons are identified.

Abstract

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 $So(n(n-1)/2-1,1)$. 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.