  In this paper we investigate charged static black holes in 4D 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.
