Matching tetrads in f(T) gravity

TL;DR

This paper discusses the method of matching tetrad fields in f(T) gravity, emphasizing the role of remnant symmetries and local Lorentz transformations in ensuring smooth junctions and spacetime parallelization.

Contribution

It provides a systematic procedure for matching tetrads in f(T) gravity using remnant symmetries, enhancing understanding of junction conditions in this theory.

Findings

Remnant symmetries are crucial for tetrad matching.

Local Lorentz transformations enable smooth junctions.

Continuity of the Weitzenböck scalar is achieved at the junction.

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\"{o}ck scalar there, even though this proves to be just a necessary condition in order to obtain a global parallelization of the spacetime.