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