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

Abstract

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 $f(T)=T+\alpha T^n$, where $\alpha$ 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.

arXiv comment11 pages, LaTeX; revised to match the version accepted for publication in Physical Review D

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• Observational Constraints on $f(T)$ gravity from varying fundamental constants
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• Galaxy-galaxy lensing data: $f(T)$ gravity challenges General Relativity
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• Black holes solutions in power-law Maxwell-$f(T)$ gravity in diverse dimensions