Weak-Field Spherically Symmetric Solutions in f(T) gravity

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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+αTⁿ, 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 ∝ r²⁻²ⁿ and discuss the impact of these perturbations in observational tests.