Spatially homogeneous Lifshitz black holes in five dimensional higher derivative gravity

TL;DR

This paper explores Lifshitz black hole solutions in five-dimensional higher derivative gravity, revealing unique properties like zero entropy at non-zero temperature and discovering new solutions in specific Bianchi classes.

Contribution

It identifies and analyzes spatially homogeneous Lifshitz black holes in higher derivative gravity, including new solutions in Bianchi Type I and IX cases.

Findings

Black holes have zero entropy at non-zero temperatures.

Solutions exist for all nine Bianchi classes in pure R^2 gravity.

New solutions found in Bianchi Type I and IX in quadratic curvature theories.

Abstract

We consider spatially homogeneous Lifshitz black hole solutions in five dimensional higher derivative gravity theories, which can be possible near horizon geometries of some systems that are interesting in the framework of gauge/gravity duality. We show the solutions belonging to the nine Bianchi classes in the pure R^2 gravity. We find that these black holes have zero entropy at non-zero temperatures and this property is the same as the case of BTZ black holes in new massive gravity at the critical point. In the most general quadratic curvature gravity theories, we find new solutions in Bianchi Type I and Type IX cases.