Phase transition and scaling behavior of topological charged black holes in Horava-Lifshitz gravity

TL;DR

This paper investigates the thermodynamic phase transitions of charged black holes in Hořava-Lifshitz gravity at the Lifshitz point, revealing a second order phase transition only for negatively curved horizons and analyzing critical behavior.

Contribution

It provides the first detailed analysis of phase transitions and critical exponents for charged black holes in Hořava-Lifshitz gravity at the Lifshitz point, highlighting the conditions for second order phase transitions.

Findings

No phase transition for flat and spherical horizons.

Second order phase transition occurs for hyperbolic horizons.

Critical exponents satisfy thermodynamic scaling laws.

Abstract

Gravity can be thought as an emergent phenomenon and it has a nice "thermodynamic" structure. In this context, it is then possible to study the thermodynamics without knowing the details of the underlying microscopic degrees of freedom. Here, based on the ordinary thermodynamics, we investigate the phase transition of the static, spherically symmetric charged black hole solution with arbitrary scalar curvature $2k$ in Ho\v{r}ava-Lifshitz gravity at the Lifshitz point $z=3$. The analysis is done using the canonical ensemble frame work; i.e. the charge is kept fixed. We find (a) for both $k=0$ and $k=1$, there is no phase transition, (b) while $k=-1$ case exhibits the second order phase transition within the {\it physical region} of the black hole. The critical point of second order phase transition is obtained by the divergence of the heat capacity at constant charge. Near the critical point, we find the various critical exponents. It is also observed that they satisfy the usual thermodynamic scaling laws.