BTZ-like black holes in even dimensional Lovelock theories

TL;DR

This paper introduces a new class of black hole solutions in even-dimensional Lovelock Born-Infeld theory, revealing complex entropy behaviors and the potential for non-zero torsion and topological charges.

Contribution

It constructs novel black hole solutions in even-dimensional Lovelock theories with non-Einstein bases, analyzing their entropy and torsion properties.

Findings

Entropies can change sign or be zero depending on base manifold geometry.

Some solutions support non-vanishing torsion.

Thermodynamical stability constrains base manifold geometry.

Abstract

In the present paper, a new class of black hole solutions is constructed in even dimensional Lovelock Born-Infeld theory. These solutions are interesting since, in some respects, they are closer to black hole solutions of an odd dimensional Lovelock Chern-Simons theory than to the more usual black hole solutions in even dimensions. This hybrid behavior arises when non-Einstein base manifolds are considered. The entropies of these solutions have been analyzed using Wald formalism. These metrics exhibit a quite non-trivial behavior. Their entropies can change sign and can even be identically zero depending on the geometry of the corresponding base manifolds. Therefore, the request of thermodynamical stability constrains the geometry of the non-Einstein base manifolds. It will be shown that some of these solutions can support non-vanishing torsion. Eventually, the possibility to define a sort of topological charge associated with torsion will be discussed.