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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 non diagonal tetrad, starting from Lagrangian in the form $f(T)=T+αT^{n}$, where $α$ is a small constant, parameterizing the departure of the theory from GR. We show that the classical spherically symmetric solutions of GR, i.e. the Schwarzschild and Schwarzschild-de Sitter solutions, are perturbed by terms in the form $\propto r^{2-2n}$ and discuss the impact of these perturbations in observational tests.