Regular black holes in $f(G)$ gravity

TL;DR

This paper explores regular charged black hole solutions within $f(G)$ gravity, extending known solutions from general relativity and analyzing their properties, including regular electric fields and energy conditions.

Contribution

It introduces a formalism for constructing regular black hole solutions in $f(G)$ gravity, including analytical forms of the $f(G)$ function, generalizing previous GR solutions.

Findings

Electric fields are always regular in these solutions.

The strong energy condition is violated inside the event horizon.

Some solutions recover GR as a special case.

Abstract

In this work, we study the possibility of generalizing solutions of regular black holes with an electric charge, constructed in general relativity, for the $f(G)$ theory, where $G$ is the Gauss-Bonnet invariant. This type of solution arises due to the coupling between gravitational theory and nonlinear electrodynamics. We construct the formalism in terms of a mass function and it results in different gravitational and electromagnetic theories for which mass function. The electric field of these solutions are always regular and the strong energy condition is violated in some region inside the event horizon. For some solutions, we get an analytical form for the $f(G)$ function. Imposing the limit of some constant going to zero in the $f(G)$ function we recovered the linear case, making the general relativity a particular case.