# P-V criticality of first-order entropy corrected AdS black holes in massive gravity

## TL;DR

This paper investigates how thermal fluctuations, modeled as logarithmic entropy corrections, influence the thermodynamics, stability, and phase transitions of four-dimensional AdS black holes in massive gravity.

## Contribution

It introduces the effect of logarithmic entropy corrections on black hole thermodynamics, revealing their necessity for stability and critical phenomena in massive gravity.

## Key findings

- Logarithmic corrections decrease thermodynamic potentials.
- Presence of corrections is essential for stability.
- Critical points depend on entropy corrections.

## Abstract

We consider a massive black hole in four dimensional AdS space and study the effect of thermal fluctuations on the thermodynamics of the black hole. We consider thermal fluctuations as logarithmic correction terms in the entropy. We analyse the effect of logarithmic correction on thermodynamics potentials like Helmholtz and Gibbs which are found decreasing functions. We study critical points and stability and find that presence of logarithmic correction is necessary to have stable phase and critical point.