Extended phase space thermodynamics of magnetized black holes with nonlinear electrodynamics

TL;DR

This paper explores the thermodynamics of magnetized black holes in AdS space coupled with nonlinear electrodynamics, revealing their horizon structure and confirming the validity of thermodynamic laws in extended phase space.

Contribution

It provides a detailed analysis of black hole thermodynamics with nonlinear electrodynamics, including the first law, Smarr relation, and thermodynamic potentials.

Findings

Black holes can have one or two horizons.

Thermodynamic laws are validated in extended phase space.

Gibbs free energy and heat capacity are computed.

Abstract

Einstein's gravity in AdS space coupled to nonlinear electrodynamics (NED) with two parameters is studied. We investigate magnetically charged black holes. The metric and mass functions and their asymptotic are obtained showing that black holes may have one or two horizons. Thermodynamics in extended phase space was studied and it was proven that the first law of black hole thermodynamics and the generalized Smarr relation hold. The magnetic potential and the vacuum polarization conjugated to coupling (NED parameter), are computed and depicted. We calculate the Gibbs free energy and heat capacity.