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

We investigate f(T) theory coupled with a nonlinear source of electrodynamics, for a spherically symmetric and static spacetime in 4D. We re-obtain the Born-Infeld and Reissner-Nordstrom-AdS solutions. We generalize the no-go theorem for any content that obeys the relationship ⁰₀=¹₁ 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)=f₀(−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)].