Issues of Lorentz-invariance in f(T) gravity and calculations for spherically symmetric solutions

TL;DR

This paper discusses the issues of Lorentz invariance in f(T) gravity, explains the covariant formulation, and demonstrates how to derive spherically symmetric solutions with simple calculations.

Contribution

It clarifies the Lorentz invariance problem in f(T) gravity and provides an accessible method for deriving spherically symmetric solutions.

Findings

Covariant formulation restores Lorentz invariance in f(T) gravity.

Explicit equations for spherically symmetric solutions are straightforward to derive.

The community's misunderstanding of covariantisation effects is addressed.

Abstract

The f(T) gravity is nowadays being widely used for cosmological model building, as well as for constructing spherically symmetric solutions. In its classical pure tetrad formulation it violates the local Lorentz symmetry in the space of tetrads. By using an appropriate spin connection it can be brought to a formally Lorentz invariant shape. However, despite some mathematical elegance obtained and new options of looking for non-standard couplings to matter probably made possible, it is fully equivalent in itself to the initial formulation. It seems that this fact, that the covariantisation does not in principle change anything, is not understood well by the community. Therefore we give a pedagogical introduction to these topics. And, on top of that, we show that obtaining the explicit equations for spherically symmetric solutions in f(T) gravity is not very difficult computationally and can be easily done even without any computer at hand.