Regular black holes in<i>f</i>(<i>T</i>) Gravity through a nonlinear electrodynamics source

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.

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