Magnetic black hole thermodynamics in an extended phase space with nonlinear electrodynamics

TL;DR

This paper explores the thermodynamics of magnetically charged black holes in Anti-de Sitter space within nonlinear electrodynamics, deriving key thermodynamic relations, analyzing phase transitions, and demonstrating finite electric fields at the origin.

Contribution

It introduces a detailed analysis of black hole thermodynamics in an extended phase space with nonlinear electrodynamics, including new mass, metric, and thermodynamic relations.

Findings

Derived the mass and metric functions for magnetically charged black holes.

Formulated the first law and generalized Smarr relation in extended phase space.

Analyzed phase transitions and stability via heat capacity and Gibbs free energy.

Abstract

We study Einstein's gravity coupled to nonlinear electrodynamics with two parameters in Anti-de Sitter spacetime. Magnetically charged black holes in an extended phase space is investigated. We obtain the mass and metric functions, their asymptotic and corrections to the Reissner--Nordstr\"{o}m metric function when the cosmological constant vanishes. The first law of black hole thermodynamics in extended phase space is formulated and the magnetic potential and the thermodynamic conjugate to the coupling are obtained. We proved the generalized Smarr relation. The heat capacity and the Gibbs free energy are computed and phase transitions are studied. It was shown that the electric field of charged objects at the origin and electrostatic self-energy are finite within the nonlinear electrodynamics proposed.