The geometrical meaning of the Weitzenböck connection

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.

8 pages; minor additions

References in corpus (7)

• Modified teleparallel gravity: inflation without inflaton
• Good and bad tetrads in f(T) gravity
• Kerr geometry in f(T) gravity
• Issues of Lorentz-invariance in f(T) gravity and calculations for spherically symmetric solutions
• Reflections on the covariance of modified teleparallel theories of gravity
• McVittie solution in f(T) gravity
• Lorentz gauge-invariant variables in torsion-based theories of gravity

Cited by in corpus (7)

• Geometry and covariance of symmetric teleparallel theories of gravity
• Static spherically symmetric solutions in New General Relativity
• Gravitational Waves in New General Relativity
• Phase space structure of symmetric teleparallel theory of gravity
• Einstein gravity from the Einstein action: Counterterms and covariance
• Weak Gravity Limit in Newer General Relativity
• More on Bianchi I spacetimes and f(T) gravity