The geometrical meaning of the Weitzenb\"ock connection

TL;DR

This paper argues that the pure tetrad formulation of modified teleparallel gravity is more fundamental and that local Lorentz invariance is not inherently natural for these theories, despite previous debates.

Contribution

It clarifies the equivalence of covariant and pure tetrad formulations and challenges the necessity of local Lorentz invariance in modified teleparallel gravity.

Findings

Pure tetrad approach is more fundamentally justified.

Local Lorentz invariance is not natural for modified teleparallel theories.

The two formulations are equivalent despite different symmetry considerations.

Abstract

In the current literature, there are many discussions about the local Lorentz invariance of modified teleparallel gravity. This symmetry is obviously violated in the classical "pure tetrad" formulation of the theory, while it gets restored in the "fully covariant" approach. My claim is that, despite many heated discussions, the two formulations are just equivalent. And the purpose of this note is to argue that the local Lorentz invariance is not natural for the modified teleparallel theories at all, making the pure tetrad approach more fundamentally justified.