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

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.

arXiv comment19 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1609.08242, arXiv:1411.7202; substantial text overlap with arXiv:1212.6128 by other authors

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• Van der Waals criticality in AdS black holes: a phenomenological study
• Black hole solutions in Gauss-Bonnet-massive gravity in the presence of power-Maxwell field
• Continuous phase transition and microstructure of charged AdS black hole with quintessence
• Can the power Maxwell nonlinear electrodynamics theory remove the singularity of electric field of point-like charges at their locations?
• Microstructure and Continuous Phase Transition of the Gauss-Bonnet AdS Black Hole
• Three-dimensional AdS black holes in massive-power-Maxwell theor
• $n+1$-dimensional Bertotti-Robinson solutions in gravity coupled with nonlinear electrodynamics