Combined effects of f(R) gravity and conformally invariant Maxwell field on the extended phase space thermodynamics of higher-dimensional black holes

TL;DR

This study explores the thermodynamics and phase transitions of higher-dimensional $f(R)$ black holes with conformally invariant Maxwell fields, revealing unique critical phenomena and confirming the universality of critical exponents.

Contribution

It provides the first detailed analysis of how $f(R)$ gravity combined with conformally invariant Maxwell fields affects black hole thermodynamics and phase behavior in higher dimensions.

Findings

Critical specific volume exists only for odd pressure p.

The ratio $P_c v_c / T_c$ differs from Einstein gravity black holes, except in 4D.

Critical exponents match those of standard AdS black holes, unaffected by $f(R)$ or Maxwell field.

Abstract

In this paper, we investigate the thermodynamics of higher-dimensional $f(R)$ black holes in the extended phase space. Both the analytic expressions and numerical results for the possible critical physical quantities are obtained. It is proved that meaningful critical specific volume only exists when $p$ is odd. This unique phenomenon may be attributed to the combined effect of $f(R)$ gravity and conformally invariant Maxwell field. It is also shown that the ratio $P_cv_c/T_c$ differs from that of higher dimensional charged AdS black holes in Einstein gravity. However, the ratio for four-dimensional $f(R)$ black holes is the same as that of four-dimensional RN-AdS black holes, implying that $f(R)$ gravity does not influence the ratio. So the ratio may be related to conformally invariant Maxwell field. To probe the phase transition, we derive the explicit expression of the Gibbs free energy with its graph plotted. Phase transition analogous to the van der Waals liquid-gas system take place between the small black hole and the large black hole. Classical swallow tail behavior, characteristic of first order phase transition, can also be observed in the Gibbs free energy graph. Critical exponents are also calculated. It is shown that these exponents are exactly the same as those of other AdS black holes, implying that neither $f(R)$ gravity nor conformally invariant Maxwell field influence the critical exponents. Since the investigated black hole solution depends on the form of the function $f(R)$, we discuss in detail how our results put constraint on the form of the function $f(R)$ and we also present a simple example.