$P-v$ criticality of a specific black hole in $f(R)$ gravity coupled with Yang-Mills field

TL;DR

This paper investigates the thermodynamic phase transitions of a specific charged AdS black hole in $f(R)$ gravity coupled with Yang-Mills field, revealing Van der Waals-like behavior and small-large black hole phase transitions.

Contribution

It demonstrates the $P-v$ criticality and phase transition behavior of a particular black hole in modified gravity with gauge field coupling, extending black hole thermodynamics studies.

Findings

Black hole exhibits Van der Waals liquid-gas phase transition.

First order phase transition between small and large black holes.

Thermodynamic properties analogous to classical thermodynamic systems.

Abstract

In this paper, we study the $P-v$ criticality of a specific charged AdS type black hole (SBH) in $f(R)$ gravity coupled with Yang-Mills field. In the extended phase space, we treat the cosmological constant as a thermodynamic pressure. After we study the various thermodynamical quantities, we show that the thermodynamic properties of the SBH behave as a Van der Waals liquid-gas system at the critical points and there is a first order phase transition between small-large SBH.