Teleparallel theories of gravity: illuminating a fully invariant approach

By Martin Krssák, R. J. Hoogen, J. G. Pereira, Christian G. Böhmer, A. Coley. Classical and quantum gravity, 2018

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Teleparallel gravity and its popular generalization gravity can be formulated as fully invariant (under both coordinate transformations and local Lorentz transformations) theories of gravity. Several misconceptions about teleparallel gravity and its generalizations can be found in the literature, especially regarding their local Lorentz invariance. We describe how these misunderstandings may have arisen and attempt to clarify the situation. In particular, the central point of confusion in the literature appears to be related to the inertial spin connection in teleparallel gravity models. While inertial spin connections are commonplace in special relativity, and not something inherent to teleparallel gravity, the role of the inertial spin connection in removing the spurious inertial effects within a given frame of reference is emphasized here. The careful consideration of the inertial spin connection leads to the construction of a fully invariant theory of teleparallel gravity and its generalizations. Indeed, it is the nature of the spin connection that differentiates the relationship between what have been called good tetrads and bad tetrads and clearly shows that, in principle, any tetrad can be utilized. The field equations for the fully invariant formulation of teleparallel gravity and its generalizations are presented and a number of examples using different assumptions on the frame and spin connection are displayed to illustrate the covariant procedure. Various modified teleparallel gravity models are also briefly reviewed.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/28bcb3280ebd8bd076a42c7c4e69b74ebeecc3f1

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In Applied Mathematics

In Astronomy and Astrophysics

Citations in the corpus

The Geometrical Trinity of Gravity (2019, background): “At least one heuristic justification for such a prescription is that by writing the pure-gauge wab μ in terms of trivial tetrads and then promoting those to the full tetrads indeed would make the pure-gauge spin connection become the metric spin connection of GR [10,12].”