# PV criticality of the second order quantum corrected Horava-Lifshitz black hole

## TL;DR

This paper examines how higher order quantum corrections influence the thermodynamics, stability, and phase transitions of Hořava-Lifshitz black holes, revealing significant effects on critical points and phase behavior.

## Contribution

It introduces second order quantum corrections to black hole thermodynamics and analyzes their impact on stability and phase transitions in specific Hořava-Lifshitz black hole solutions.

## Key findings

- Higher order corrections modify critical points.
- Quantum effects influence black hole stability.
- Second order phase transition observed in Kehagius-Sfetsos solution.

## Abstract

In this paper, higher order quantum gravity effects on the thermodynamics of Ho\v{r}ava-Lifshitz black hole investigated. Both Kehagius-Sfetsos and Lu-Mei-Pop solutions of Ho\v{r}ava-Lifshitz black hole considered and higher order corrected thermodynamics quantities obtained. The first order correction is logarithmic and second order correction considered proportional to the inverse of entropy. These corrections are due to the thermal fluctuation and interpreted as quantum loop corrections. Effect of such quantum corrections on the stability and critical points of Horava-Lifshitz black holes studied. We find that higher order correction affects critical point and stability of Lu-Mei-Pop solution and yield to the second order phase transition for the case of Kehagius-Sfetsos solution.