Phase transition and thermodynamic stability in extended phase space and charged Ho\v{r}ava-Lifshitz black holes

TL;DR

This paper investigates phase transitions and thermodynamic stability of charged Horava-Lifshitz black holes in extended phase space, analyzing their nature, stability criteria, and geometric properties to understand their critical behavior.

Contribution

It demonstrates the second order phase transition at a sharp temperature, verifies Ehrenfest equations, and explores thermodynamic geometry in the context of Horava-Lifshitz black holes.

Findings

Second order phase transition occurs at a sharp temperature.

Ehrenfest equations are satisfied, confirming the phase transition nature.

Thermodynamic geometry reveals scalar curvature behavior consistent with phase transition.

Abstract

For charged black holes in Horava-Lifshitz gravity, a second order phase transition takes place in extended phase space where the cosmological constant is taken as thermodynamic pressure. We relate the second order nature of phase transition to the fact that the phase transition occurs at a sharp temperature and not over a temperature interval. Once we know the continuity of the first derivatives of the Gibbs free energy, we show that all the Ehrenfest equations are readily satisfied. We study the effect of the perturbation of the cosmological constant as well as the perturbation of the electric charge on thermodynamic stability of Horava-Lifshitz black hole. We also use thermodynamic geometry to study phase transition in extended phase space. We investigate the behavior of scalar curvature of Weinhold, Ruppeiner, and Quevedo metric in extended phase space of charged Horava-Lifshitz black holes. It is checked if these curvatures could reproduce the result of specific heat for the phase transition.