Regular model of magnetized black hole with rational nonlinear electrodynamics

TL;DR

This paper presents a regular magnetized black hole model based on rational nonlinear electrodynamics, showing non-singular core, thermodynamic stability, and bounded curvature invariants, extending classical solutions with quantum gravity considerations.

Contribution

It introduces a modified Hayward metric with rational nonlinear electrodynamics, incorporating quantum gravity effects and analyzing thermodynamic properties and curvature bounds.

Findings

Black hole has a de Sitter core without singularities.

Thermodynamic phase transitions occur, with stability at certain horizons.

Curvature invariants are bounded, supporting the limiting curvature conjecture.

Abstract

A modified Hayward metric of magnetically charged black hole space-time based on rational nonlinear electrodynamics with the Lagrangian ${\cal L} = -{\cal F}/(1+2\beta{\cal F})$ is considered. We introduce the fundamental length, characterizing quantum gravity effects. If the fundamental length vanishes the general relativity coupling to rational nonlinear electrodynamics is recovered. We obtain corrections to the Reissner--Nordstr\"{o}m solution as the radius approaches infinity. The metric possesses a de Sitter core without singularities as $r\rightarrow 0$. The Hawking temperature and the heat capacity are calculated. It was shown that phase transitions occur and black holes are thermodynamically stable at some event horizon radii. We demonstrate that curvature invariants are bounded and the limiting curvature conjecture takes place.