Exact Solutions of Lovelock-Born-Infeld Black Holes

TL;DR

This paper presents exact five-dimensional Lovelock-Born-Infeld black hole solutions, analyzing their properties, stability, and similarities to lower-dimensional black holes, contributing new explicit solutions in modified gravity theories.

Contribution

It provides the first exact five-dimensional charged black hole solutions in Lovelock gravity coupled with Born-Infeld electrodynamics, exploring their thermodynamics and stability.

Findings

The solutions interpolate between known black holes in Einstein-Born-Infeld and Lovelock theories.

Proper parameter choices remove conical singularities at the origin.

The specific heat behavior indicates a stability transition point.

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.