Abstract
In this paper we investigate charged static black holes in 4 D for generalized teleparallel models of gravity, based on torsion as the geometric object for describing gravity according to the equivalence principle. As a motivated idea, we introduce a set of non-diagonal tetrads and derive the full system of non linear differential equations. We prove that the common Schwarzschild gauge is applicable only when we study linear f ( T ) case. We reobtain the Reissner-Nordstrom-de Sitter (or RN-AdS) solution for the linear case of f ( T ) and perform a parametric cosmological reconstruction for two nonlinear models. We also study in detail a type of the no-go theorem in the framework of this modified teleparallel gravity.