Junction conditions in extended Teleparallel gravities

TL;DR

This paper investigates the junction conditions in extended Teleparallel gravity theories, revealing stricter requirements than in General Relativity and highlighting the importance of torsion continuity for standard solutions.

Contribution

It derives the specific junction conditions in extended Teleparallel gravity and shows how they differ from those in General Relativity, emphasizing the role of torsion continuity.

Findings

Junction conditions are more restrictive than in GR.

Continuity of scalar torsion is necessary for standard solutions.

New conditions on tetrads prevent delta-like distributions.

Abstract

In the context of extended Teleparallel gravity theories, we address the issue of junction conditions required to guarantee the correct matching of different regions of spacetime. In the absence of shells/branes, these conditions turn out to be more restrictive than their counterparts in General Relativity as in other extended theories of gravity. In fact, the general junction conditions on the matching hypersurfaces depend on the underlying theory and a new condition on the induced tetrads in order to avoid delta-like distributions in the field equations. This result imposes strict consequences on the viability of standard solutions such as the Einstein-Straus-like construction. We find that the continuity of the scalar torsion is required in order to recover the usual General Relativity results.