$P-V$ criticality of AdS black hole in $f(R)$ gravity

TL;DR

This paper investigates how $f(R)$ gravity modifications affect the thermodynamics and phase transitions of charged AdS black holes, revealing that $f(R)$ influences free energy and critical behavior while preserving universal critical exponents.

Contribution

It demonstrates the impact of $f(R)$ corrections on black hole thermodynamics and phase transitions, highlighting the monotonic change of the critical ratio and the invariance of critical exponents.

Findings

$f(R)$ correction alters Gibbs free energy and phase transition characteristics.

The critical ratio $ ho_c$ increases monotonically with $f'(R_0)$.

Critical exponents remain the same as in the Van der Waals fluid.

Abstract

We study thermodynamics of a charged AdS black hole in the special $f(R)$ correction with the constant Ricci scalar curvature. Our results show that the the $f(R)$ correction influences the Gibbs free energy and the phase transition of system. The ratio $\rho_c$ occurred at the critical point increases monotonically with the derivative term $f'(R_0)$. We also disclose that the critical exponents are the same as those of the liquid-gas phase transition in the Van der Waals model, which does not depend on the $f(R)$ correction considered here.