Regular black holes in $f(T)$ Gravity through a nonlinear electrodynamics source

TL;DR

This paper introduces a new class of exact regular black hole solutions in $f(T)$ gravity with nonlinear electrodynamics, demonstrating finite geometric scalars at the origin and extending solutions beyond General Relativity.

Contribution

It develops a novel method to find exact solutions in $f(T)$ gravity, including the first regular black holes with all scalar invariants finite at the center.

Findings

First class of regular black holes in $f(T)$ gravity with finite scalars at the origin.

Recovery of General Relativity solutions when $f(T)=T$.

Identification of new singular black hole solutions.

Abstract

We seek to obtain a new class of exact solutions of regular black holes in $f(T)$ Gravity with non-linear electrodynamics material content, with spherical symmetry in $4D$. The equations of motion provide the regaining of various solutions of General Relativity, as a particular case where the function $f(T)=T$. We developed a powerful method for finding exact solutions, where we get the first new class of regular black holes solutions in the $f(T)$ Theory, where all the geometrics scalars disappear at the origin of the radial coordinate and are finite everywhere, as well as a new class of singular black holes.