Lovelock-Lifshitz Black Holes

TL;DR

This paper explores Lifshitz solutions in Lovelock gravity, deriving exact black hole solutions with Lifshitz asymptotics, analyzing their thermodynamics, and presenting rotating black hole solutions, thus extending the understanding of higher-curvature gravity models.

Contribution

It provides the first exact Lifshitz black hole solutions in Lovelock gravity and analyzes their thermodynamics and stability properties.

Findings

Exact Lifshitz black hole solutions in Gauss-Bonnet and third-order Lovelock gravity.

Lifshitz solutions are sensitive to Lovelock corrections, more so than AdS solutions.

Large black holes with curved horizons have temperature proportional to $r_0^z$, with no unstable phases.

Abstract

In this paper, we investigate the existence of Lifshitz solutions in Lovelock gravity, both in vacuum and in the presence of a massive vector field. We show that the Lovelock terms can support the Lifshitz solution provided the constants of the theory are suitably chosen. We obtain an exact black hole solution with Lifshitz asymptotics of any scaling parameter $z$ in both Gauss-Bonnet and in pure 3rd order Lovelock gravity. If matter is added in the form of a massive vector field, we also show that Lifshitz solutions in Lovelock gravity exist; these can be regarded as corrections to Einstein gravity coupled to this form of matter. For this form of matter we numerically obtain a broad range of charged black hole solutions with Lifshitz asymptotics, for either sign of the cosmological constant. We find that these asymptotic Lifshitz solutions are more sensitive to corrections induced by Lovelock gravity than are their asymptotic AdS counterparts. We also consider the thermodynamics of the black hole solutions and show that the temperature of large black holes with curved horizons is proportional to $r_0^z$ where $z$ is the critical exponent; this relationship holds for black branes of any size. As is the case for asymptotic AdS black holes, we find that an extreme black hole exists only for the case of horizons with negative curvature. We also find that these Lovelock-Lifshitz black holes have no unstable phase, in contrast to the Lovelock-AdS case. We also present a class of rotating Lovelock-Lifshitz black holes with Ricci-flat horizons.