Non-Abelian Lovelock-Born-Infeld Topological Black Holes

TL;DR

This paper explores new asymptotically AdS black hole solutions in higher-dimensional Einstein gravity with non-Abelian Born-Infeld fields, revealing unique properties related to mass, charge, and singularity types compared to Einstein-Yang-Mills solutions.

Contribution

It introduces novel non-Abelian Lovelock-Born-Infeld black hole solutions, analyzing their properties and asymptotic behaviors across various dimensions, extending previous Einstein-Yang-Mills models.

Findings

Solutions differ in mass, charge, and singularity nature from Einstein-Yang-Mills black holes.

Existence of extremal black holes with non-negative mass in Einstein-Yang-Mills-Born-Infeld theory.

Singularity types can be timelike or spacelike depending on parameters and dimensions.

Abstract

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.