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

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.