Matching tetrads in f(T) gravity

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 ${\mathcal{C}}^1$-match the corresponding tetrads on the junction surface. This automatically ensures the continuity of the Weitzenb"{o}ck scalar there, even though this proves to be just a necessary condition in order to obtain a global parallelization of the spacetime.