Born--Infeld-type electrodynamics and magnetic black holes

TL;DR

This paper explores a nonlinear electrodynamics model coupled with gravity, producing regular magnetic black holes with finite charge self-energy, analyzing their solutions, asymptotics, and thermodynamic stability.

Contribution

It introduces a Born--Infeld-type nonlinear electrodynamics model with three parameters, demonstrating regular magnetic black hole solutions and their thermodynamic properties.

Findings

Black holes can be regular for certain parameters.

The model yields finite charge self-energy.

Black holes exhibit phase transitions and are thermodynamically unstable.

Abstract

We investigate a Born--Infeld-type model of nonlinear electrodynamics, possessing three parameters, coupled with general relativity. As a particular case Born--Infeld electrodynamics is reproduced. There is no singularity of the electric field at the centre of point-like charged particles and self-energy of charges is finite in this model. The magnetized black hole is studied and solutions are obtained. We demonstrate that for some parameters of the model the black hole is regular. We find the asymptotic of the metric and mass functions at $r\rightarrow\infty$ and $r\rightarrow 0$, and corrections to the Reissner--Nordstr\"{o}m solution. Thermodynamics of black holes is investigated. We calculate the Hawking temperature of black holes and show that black holes are not stable and there are phase transitions in the model under consideration.