On a model of magnetically charged black hole with nonlinear electrodynamics

TL;DR

This paper explores a nonlinear electrodynamics model for magnetically charged black holes, revealing corrections to classical solutions, horizon structures, and thermodynamic stability, including phase transitions.

Contribution

It introduces a specific nonlinear electrodynamics model affecting black hole solutions and thermodynamics, extending the Reissner-Nordström solution with new stability insights.

Findings

Corrections to Reissner-Nordström solution

Existence of one, two, or no horizons depending on parameters

Black hole thermodynamic stability and phase transitions

Abstract

The Bronnikov model of nonlinear electrodynamics is investigated in general relativity. The magnetic black hole is considered and we obtain a solution giving corrections to the Reissner-Nordstr\"{o}m solution. In this model spacetime at $r\rightarrow\infty$ becomes Minkowski's spacetime. We calculate the magnetic mass of the black hole and the metric function. At some parameters of the model there can be one, two or no horizons. The Hawking temperature and the heat capacity of black holes are calculated. We show that a second-order phase transition takes place and black holes are thermodynamically stable at some range of parameters.