Maxwell's equal area law for black holes in power Maxwell invariant

TL;DR

This paper investigates the phase transition behavior of black holes in power Maxwell invariant theories using Maxwell's equal area law, revealing small-large black hole transitions analogous to classical thermodynamic systems.

Contribution

It extends the application of Maxwell's equal area law to black holes in power Maxwell invariant theories and explores phase transitions in different thermodynamic ensembles.

Findings

Black holes exhibit small-large phase transitions similar to Van der Waals fluids.

Phase transition occurs in both canonical and grand canonical ensembles.

Black hole parameters influence the two-phase coexistence conditions.

Abstract

In this paper, we consider the phase transition of black hole in power Maxwell invariant by means of Maxwell's equal area law. First, we review and study the analogy of nonlinear charged black hole solutions with the Van der Waals gas-liquid system in the extended phase space, and obtain isothermal $P$-$v$ diagram. Then, using the Maxwell's equal area law we study the phase transition of AdS black hole with different temperatures. Finally, we extend the method to the black hole in the canonical (grand canonical) ensemble in which charge (potential) is fixed at infinity. Interestingly, we find the phase transition occurs in the both ensembles. We also study the effect of the parameters of the black hole on the two-phase coexistence. The results show that the black hole may go through a small-large phase transition similar to those of usual non-gravity thermodynamic systems.