Bianchi identities in f(T) gravity: paving the way to confrontation with astrophysics

TL;DR

This paper clarifies the structure of spherically symmetric solutions in $f(T)$ gravity, demonstrating their equivalence in different approaches and establishing the consistency of Bianchi identities, thereby strengthening the theoretical foundation for astrophysical applications.

Contribution

It shows the equivalence of two approaches to spherically symmetric solutions in $f(T)$ gravity and confirms the compatibility of Bianchi identities within this framework.

Findings

Two approaches to spherically symmetric solutions are fully equivalent.

Bianchi identities in $f(T)$ gravity are compatible with the field equations.

The results provide a firmer theoretical basis for astrophysical tests of $f(T)$ gravity.

Abstract

Theories of $f(T)$ gravity are being actively confronted with cosmological observations, and are being studied for their potential to solve famous problems of cosmology. A necessary step is to extend these studies to astrophysical settings. However, to this end one must understand the structure of spherically symmetric solutions. We show that two different known approaches to these solutions are actually fully equivalent from the point of view of Lorentz-covariant formalism. Moreover, we explain Bianchi identities in $f(T)$ gravity and apply them to show that the corresponding equations are always compatible. It puts these efforts on much firmer grounds than before.