Extended phase space thermodynamics and P-V criticality of black holes with nonlinear source

TL;DR

This paper explores the thermodynamics and phase transitions of black holes with nonlinear electromagnetic sources in extended phase space, revealing novel phase behavior and universal ratios similar to classical thermodynamics.

Contribution

It introduces the analysis of black hole solutions with power Maxwell invariant sources, highlighting phase transitions in both canonical and grand canonical ensembles, unlike standard Maxwell black holes.

Findings

Phase transitions occur in both ensembles, unlike Maxwell black holes.

Critical exponents match mean field theory predictions.

Universal ratio $rac{P_{c}v_{c}}{T_{c}}$ is dimension-independent.

Abstract

In this paper, we consider the solutions of Einstein gravity in the presence of a generalized Maxwell theory, namely power Maxwell invariant. First, we investigate the analogy of nonlinear charged black hole solutions with the Van der Waals liquid--gas system in the extended phase space where the cosmological constant appear as pressure. Then, we plot isotherm $P$--$V$ diagram and study the thermodynamics of AdS black hole in the (grand canonical) canonical ensemble in which (potential) charge is fixed at infinity. Interestingly, we find the phase transition occurs in the both of canonical and grand canonical ensembles in contrast to RN black hole in Maxwell theory which only admits canonical ensemble phase transition. Moreover, we calculate the critical exponents and find their values are the same as those in mean field theory. Besides, considerably, we find in the grand canonical ensembles universal ratio $\frac{P_{c}v_{c}}{T_{c}}$ is independent of spacetime dimensions.