paper

The covariant formulation of f(T) gravity

arXiv:1510.08432 · doi:10.1088/0264-9381/33/11/115009

Abstract

We show that the well-known problem of frame dependence and violation of local Lorentz invariance in the usual formulation of gravity is a consequence of neglecting the role of spin connection. We re-formulate gravity starting, instead of the "pure-tetrad" teleparallel gravity, from the covariant teleparallel gravity, using both the tetrad and the spin connection as dynamical variables, resulting in the fully covariant, consistent, and frame-independent, version of gravity, which does not suffer from the notorious problems of the usual, pure-tetrad, theory. We present the method to extract solutions for the most physically important cases, such as the Minkowski, the FRW and the spherically-symmetric ones. We show that in the covariant gravity we are allowed to use an arbitrary tetrad in an arbitrary coordinate system along with the corresponding spin connection, resulting always to the same physically relevant field equations.

12 pages, version published in CQG

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