Born-Infeld and charged black holes with non-linear source inf(T) gravity

We investigate f ( T ) theory coupled with a nonlinear source of electrodynamics, for a spherically symmetric and static spacetime in 4 D . We re-obtain the Born-Infeld and Reissner-Nordstrom-AdS solutions. We generalize the no-go theorem for any content that obeys the relationship 0 0 = 1 1 for the energy-momentum tensor and a given set of tetrads. Our results show new classes of solutions where the metrics are related through b ( r )=− Na ( r ). We do the introductory analysis showing that solutions are that of asymptotically flat black holes, with a singularity at the origin of the radial coordinate, covered by a single event horizon. We also reconstruct the action for this class of solutions and obtain the functional form f ( T )= f 0 (− T ) ( N +3)/[2( N +1)] and NED = 0 (− F ) ( N +3)/[2( N +1)] . Using the Lagrangian density of Born-Infeld, we obtain a new class of charged black holes where the action reads f ( T )=−16β BI [1−√1+( T /4β BI )].