Regular black holes in $f(R)$ gravity coupled to nonlinear electrodynamics

TL;DR

This paper derives a new class of regular black hole solutions within $f(R)$ gravity coupled to nonlinear electrodynamics, generalizing known solutions in general relativity and analyzing their physical properties.

Contribution

It introduces a one-parameter family of regular black hole solutions in $f(R)$ gravity with nonlinear electrodynamics, extending previous GR solutions and exploring their energy conditions.

Findings

Solutions reduce to known GR black holes when parameter vanishes

Some solutions violate the strong energy condition

Regularity of the black holes is thoroughly analyzed

Abstract

We obtain a class of regular black hole solutions in four-dimensional $f(R)$ gravity, $R$ being the curvature scalar, coupled to a nonlinear electromagnetic source. The metric formalism is used and static spherically symmetric spacetimes are assumed. The resulting $f(R)$ and nonlinear electrodynamics functions are characterized by a one-parameter family of solutions which are generalizations of known regular black holes in general relativity coupled to nonlinear electrodynamics. The related regular black holes of general relativity are recovered when the free parameter vanishes, in which case one has $f(R)\propto R$. We analyze the regularity of the solutions and also show that there are particular solutions that violate only the strong energy condition