Phase transitions in four-dimensional AdS black holes with a nonlinear electrodynamics source

TL;DR

This paper investigates the thermodynamic phase transitions of four-dimensional AdS black holes influenced by a nonlinear power-law electromagnetic field, revealing both first and second order transitions depending on the ensemble.

Contribution

It introduces the analysis of phase transitions in AdS black holes with nonlinear electrodynamics, highlighting ensemble-dependent thermodynamic behaviors.

Findings

Both first and second order phase transitions occur in the canonical ensemble.

Hawking-Page and second order phase transitions are observed in the grand canonical ensemble.

Nonlinear electrodynamics affects the nature of thermodynamic phase transitions.

Abstract

In this work we consider black hole solutions to Einstein theory coupled to a nonlinear power-law electromagnetic field with a fixed exponent value. We study the extended phase space thermodynamics in canonical and grand canonical ensembles where the varying cosmological constant plays the role of an effective thermodynamic pressure. We examine thermodynamical phase transitions in such black hols and find that both first and second order phase transitions can occur in the canonical ensemble, while for the grand canonical ensemble the Hawking-Page and second order phase transitions are allowed.