Non-Abelian Lovelock-Born-Infeld Topological Black Holes

We present the asymptotically AdS solutions of the Einstein gravity with hyperbolic horizons in the presence of $So(n(n-1)/2-1, 1)$ Yang-Mills fields governed by the non-Abelian Born-Infeld lagrangian. We investigate the properties of these solutions as well as their asymptotic behavior in varies dimensions. The properties of these kind of solutions are like the Einstein-Yang-Mills solutions. But the differences seems to appear in the role of the mass, charge and born-Infeld parameter $\beta$, in the solutions. For example in Einstein-Yang-Mills theory the solutions with non-negative mass cannot present an extreme black hole while that of in Einstein-Yang-Mills-Born Infeld theory can. Also the singularities in higher dimensional Einstein-Yang-Mills theory for non-negative mass are always spacelike, while depending on choosing the parameters, we can find timelike singularities in the similar case of Einstein-Yang-Mills-Born-Infeld theory. We also extend the solutions of Einstein to the case of Gauss-Bonnet and Lovelock gravity. It is shown that, these solutions in the limits of $\beta\to0$, and $\beta\to\infty$, represent pure gravity and gravity coupled with Yang-Mills fields, respectively.