Black Hole Thermodynamics in Horava Lifshitz Gravity and the Related Geometry

TL;DR

This paper explores black hole thermodynamics within Hořava-Lifshitz gravity, analyzing different entropy functions and investigating the possibility of phase transitions, thereby enhancing understanding of black hole behavior in non-relativistic gravity theories.

Contribution

It introduces a detailed thermodynamic analysis of black holes in Hořava-Lifshitz gravity using classical and topological entropy functions, and examines phase transition possibilities.

Findings

Different entropy functions affect black hole thermodynamics.

Phase transitions are analyzed for these black holes.

The study clarifies thermodynamic stability in this gravity model.

Abstract

Recently, Ho$\breve{r}$ava proposed a non-relativistic renormalizable theory of gravity which is essentially a field theoretic model for a UV complete theory of gravity and reduces to Einstein gravity with a non-vanishing cosmological constant in IR. Also the theory admits a Lifshitz scale-invariance in time and space with broken Lorentz symmetry at short scale. On the other hand, at large distances higher derivative terms do not contribute and the theory coincides with general relativity. Subsequently, Cai and his collaborators and then Catiuo et al have obtained black hole solutions in this gravity theory and studied the thermodynamic properties of the black hole solution. In the present paper, we have investigated the black hole thermodynamic for two choices of the entropy function - a classical and a topological in nature. Finally, it is examined whether a phase transition is possible or not.