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.

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

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• Revisiting diagonal tetrads: New Black Hole solutions in $f(T)$ gravity
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• Linearized modified gravity theories and gravitational waves physics in the GBD theory
• Geodesic Congruences and a Collapsing Stellar Distribution in f (T ) Theories
• New proper tetrad for teleparallel gravities in non-flat spacetime
• Effect of some modified models of gravity on the radial velocity of binary systems
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• Parametrized post-Newtonian formalism in higher-order Teleparallel Gravity
• Black holes solutions in power-law Maxwell-$f(T)$ gravity in diverse dimensions