Weak-field spherically symmetric solutions in f (T) gravity

We study weak-field solutions having spherical symmetry in f(T) gravity; to this end, we solve the field equations for a nondiagonal tetrad, starting from Lagrangian in the form f(T) = T + alpha T-n, where alpha is a small constant, parametrizing the departure of the theory from general relativity. We show that the classical spherically symmetric solutions of general relativity, i.e., the Schwarzschild and Schwarzschild-de Sitter solutions, are perturbed by terms in the form alpha r(2-2n) and discuss the impact of these perturbations in observational tests.