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

TL;DR

This paper investigates weak-field spherically symmetric solutions in $f(T)$ gravity, analyzing how small deviations from General Relativity modify classical solutions and their observational implications.

Contribution

It derives perturbed Schwarzschild solutions in $f(T)$ gravity with a specific Lagrangian form, highlighting deviations from GR.

Findings

Classical solutions are perturbed by terms proportional to $r^{2-2n}$.

Perturbations impact observational tests of gravity.

The study provides a framework for testing $f(T)$ gravity in weak-field regimes.

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.