Approaches to spherically symmetric solutions in f(T) gravity

TL;DR

This paper investigates static spherically symmetric solutions in f(T) gravity, simplifying the search to two key equations, enabling the derivation of exact and approximate solutions across different f(T) models.

Contribution

It introduces a reduction method for finding solutions in f(T) gravity, separating the problem into a model-independent equation and a radial one for specific f functions.

Findings

Derived a universal equation independent of f(T)

Formulated a radial equation to identify suitable f functions

Obtained exact and perturbative solutions for various f(T) models

Abstract

We study properties of static spherically symmetric solutions in $f(\mathbb T)$ gravity. Based on our previous work on generalising Bianchi identities for this kind of theories, we show how this search of solutions can be reduced to the study of two relatively simple equations. One of them does not depend on the function $f$ and therefore describes the properties of such solutions in any $f(\mathbb T)$ theory. Another equation is the radial one and, if a possible solution is chosen, it allows to find out which function $f$ is suitable for it. We use these equations to find exact and perturbative solutions for arbitrary and specific choices off.