Good and bad tetrads in f(T) gravity

By Nicola Tamanini, C. Boehmer. 2012

236 citations recorded by the source corpus.

We investigate the importance of choosing good tetrads for the study of the field equations of $f(T)$ gravity. It is well known that this theory is not invariant under local Lorentz transformations, and therefore the choice of tetrad plays a crucial role in such models. Different tetrads will lead to different field equations which in turn have different solutions. We suggest to speak of a good tetrad if it imposes no restrictions on the form of $f(T)$. Employing local rotations, we construct good tetrads in the context of homogeneity and isotropy, and spherical symmetry, where we show how to find Schwarzschild-de Sitter solutions in vacuum. Our principal approach should be applicable to other symmetries as well.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a62a6891d2ae3c4d13e5abaa6fa72cdb5a832761

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Citations in the corpus

Teleparallel Palatini theories (2018, methodology): “The situation is analogous with the usual teleparallel torsion theories, where though the inertial connection could be set to zero by a suitable Lorentz transformation, the additional degrees of freedom decouple from the theory only when the action supports an additional Lorentz symmetry so that the”
Cosmological perturbations in modified teleparallel gravity models (2018, background): “eneous, contradicting the symmetries of the background. A general T-dependent action won’t thus allow any non-trivial solutions for this background. This means that the diagonal tetrads are no ”good” [28] i.e. not compatible with the zero spin connection as explained in [20]. Following the original ”
f(T) teleparallel gravity and cosmology (2015, methodology): “We stress that the field equations of covariant f(T ) gravity [128], generated from the diagonal tetrad (317) and the non-zero spin connection (318), coincide with those obtained in the usual, noncovariant, formulation of f(T ) gravity, for zero spin connection but for the specific and peculiar nond”
Teleparallel theories of gravity: illuminating a fully invariant approach (2018, methodology): “In the framework of f(T ) gravity, this problem was considered in [41, 46, 75–85].”
On the covariance of teleparallel gravity theories (2017, background): “In other words, the formulation with arbitrary inertial spin connection resolves the issue of ”good and bad tetrads” [12].”