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Proceedings 2018, 2(1), 33;

Good vs. Bad Tetrads in f(T) Gravity and the Role of Spacetime Symmetries

Laboratory of Theoretical Physics, Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia
Presented at Symmetry 2017—The First International Conference on Symmetry, Barcelona, Spain, 16–18 October 2017.
Published: 9 January 2018
(This article belongs to the Proceedings of Symmetry 2017)
PDF [162 KB, uploaded 11 April 2018]


It is well known that the field equations of f(T) gravity break local Lorentz invariance if one a priori assumes a vanishing spin connection, except in the teleparallel equivalent of general relativity (TEGR) case f(T) = T + Λ. One consequence is the existence of “bad” tetrads, i.e., tetrads which force a constraint on the field equations, which can be satisfied only in the TEGR case, hence prohibiting any modification of the gravitational dynamics. In order to overcome this difficulty, one may either restrict oneself to “good” tetrads, from which no such constraint arises, or introduce a suitable spin connection, which cancels the constraint. However, there is no simple procedure or general formula for these good tetrads or suitable spin connections, and only particular examples have been constructed. I will show how spacetime symmetries act on good and bad tetrads, and can be used to distinguish them, hence giving a simpler criterion for good tetrads. I will also show how a sufficiently high amount of symmetry can be used to determine either the good tetrads or the required spin connection.
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Hohmann, M. Good vs. Bad Tetrads in f(T) Gravity and the Role of Spacetime Symmetries. Proceedings 2018, 2, 33.

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