Matching tetrads in f (T) gravity

Abstract

The procedure underlying the matching of 1-form (tetrad) fields in theories possessing absolute parallelism - f(T) gravity being within this category - is addressed and exemplified. We show that the remnant symmetries of the intervening spaces play a central role in the process, because the knowledge of the remnant group of local Lorentz transformations enables one to perform rotations and/or boosts in order to C1-match the corresponding tetrads on the junction surface. This automatically ensures the continuity of the Weitzenböck scalar there, even though this proves to be just a necessary condition in order to obtain a global parallelization of the spacetime.