# The temperature and entropy corrections on the charged hairy black holes

## TL;DR

This paper studies how first-order entropy and temperature corrections, due to thermal fluctuations, affect the thermodynamics, stability, and phase transitions of charged hairy black holes.

## Contribution

It introduces first-order thermal fluctuation corrections to black hole thermodynamics and analyzes their impact on phase behavior and stability.

## Key findings

- Thermal fluctuations influence black hole stability.
- Corrections modify critical points and phase transition behavior.
- Comparison shows significant differences between corrected and uncorrected thermodynamics.

## Abstract

In this paper, we consider the first order correction of the entropy and temperature in a charged black hole with a scalar field. Here, we apply such correction for the different cases of black holes. These corrections are due to the thermal fluctuations of statistical physics. Also, we take advantage of such corrections and study the $ P - V $ critically and phase transition. Also, we investigate the effect of correction on the critical point and stability of the system. We obtain modified thermodynamics quantities and find effects of thermal fluctuations in the stability of the black hole. We find that stability of black hole is depend on the thermal fluctuations. Finally, we compare the results of the corrected and uncorrected by thermodynamical quantities.