Exact Solutions of Lovelock-Born-Infeld Black Holes

Abstract

The exact five-dimensional charged black hole solution in Lovelock gravity coupled to Born-Infeld electrodynamics is presented. This solution interpolates between the Hoffmann black hole for the Einstein-Born-Infeld theory and other solutions in the Lovelock theory previously studied in the literature. The conical singularity of the metric around the origin can be removed by a proper choice of the black hole parameters. The thermodynamic properties of the solution are also analyzed and, in particular, it is shown that the behaviour of the specific heat indicates the existence of a stability transition point in the vacuum solutions. We discuss the similarities existing between this five-dimensional geometry and the three-dimensional black hole. Like BTZ black hole, the Lovelock black hole has an infinite lifetime.