Matching tetrads in f(T) gravity

Understand

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.