Non-abelian lovelock-born-infeld topological black holes

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 are presented. We investigate the properties of these solutions as well as their asymptotic behavior in various dimensions. The properties of these kinds of solutions are like the Einstein-Yang-Mills solutions. But the differences seem 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 third order Lovelock gravities. It is shown that, these solutions in the limits of beta -> 0, and beta ->infinity, represent pure gravity and gravity coupled with Yang-Mills fields, respectively.