Weak-field spherically symmetric solutions in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>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 $f(T)=T+\ensuremath{\alpha}{T}^{n}$, where $\ensuremath{\alpha}$ 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 $\ensuremath{\propto}{r}^{2\ensuremath{-}2n}$ and discuss the impact of these perturbations in observational tests.

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