Remarks on nonsingular models of Hayward and magnetized black hole with rational nonlinear electrodynamics

TL;DR

This paper explores nonsingular Hayward and magnetized black hole models within rational nonlinear electrodynamics, demonstrating de Sitter cores, analyzing thermodynamic properties, and questioning the gravity source in the Hayward model.

Contribution

It introduces and analyzes nonsingular black hole solutions based on rational nonlinear electrodynamics, highlighting their thermodynamic behavior and questioning the gravity source in the Hayward model.

Findings

Black hole metrics have de Sitter cores without singularities.

Thermodynamic properties show phase transitions at temperature maxima.

The source of gravity in the Hayward model is questionable.

Abstract

A Hayward black hole and magnetically charged black hole based on rational nonlinear electrodynamics with the Lagrangian ${\cal L} = -{\cal F}/(1+2\beta{\cal F})$ (${\cal F}$ is a field invariant) are considered. It was shown that the metric function in both models possesses a de Sitter core without singularities as $r\rightarrow 0$. The behavior of the Hawking temperature and the heat capacity in these models are similar. The phase transitions take place when the Hawking temperature has a maximum, and black holes are thermodynamically stable at some event horizon radii when the heat capacity is positive. We show that the source of gravity in the Hayward model is questionable.