Lifshitz black holes in the Ho\v{r}ava-Lifshitz gravity

TL;DR

This paper explores Lifshitz black hole solutions within Hořava-Lifshitz gravity, comparing their properties to those from 3D new massive gravity, and analyzes their thermodynamics and phase transition possibilities.

Contribution

It provides a comparative analysis of Lifshitz black holes in Hořava-Lifshitz gravity and 3D new massive gravity, highlighting their thermodynamic similarities and phase transition behavior.

Findings

All solutions have single horizons.

Black holes exhibit similar thermodynamic properties.

Second order phase transitions between certain Lifshitz black holes are unlikely.

Abstract

We investigate the Lifshitz black holes from the Ho\v{r}ava-Lifshitz gravity by comparing with the Lifshitz black hole from the 3D new massive gravity. We note that these solutions all have single horizons. These black holes are very similar to each other when studying their thermodynamics. It is shown that a second order phase transition is unlikely possible to occur between $z=3,2$ Lifshitz black holes and $z=1$ Ho\v{r}ava black hole.