Consequences of Thermal Fluctuations of Well-Known Black Holes in Modified Gravity

TL;DR

This paper investigates how thermal fluctuations influence the stability and phase transitions of various black holes in modified gravity, providing detailed thermodynamic analysis and stability criteria.

Contribution

It introduces a comprehensive thermodynamic framework for black holes with thermal fluctuations in modified gravity, including new stability and phase transition insights.

Findings

Thermal fluctuations affect black hole stability.

Phase transition points depend on parameters like ta, m, and ta.

Black holes exhibit both local and global stability under certain conditions.

Abstract

Quantum fluctuation consequences have significant role in high-energy physics. These fluctuation often regarded as a correction of the infrared (IR) limit. Such correction contribute to the high-energy limit of thermodynamical quantities and the stability conditions of black holes. In this work, we analyze the thermal stability of black holes in the presence of thermal fluctuations. We consider AdS black hole in Born-Infeld massive gravity with non-abelian hair and the charged AdS black hole with a global monopole. We develop many thermodynamical quantities such as entropy, temperature, pressure, heat capacity of a system at constant volume and pressure, ratio between the heat capacities at constant pressure and volume, Gibbs free energy and Helmholtz free energy for both black holes. The critical behavior and phase transitions of black holes are also presented. We also observe the local and global stability of black holes in the grand canonical ensemble and canonical ensemble for the specific values of different parameters, such as, symmetry breaking parameter $\eta$, massive parameter $m$ and non-abelian hair $\nu$.