Junction Conditions for F(T) Gravity from a Variational Principle

We derive a general set of acceptable junction conditions for $F(T)$ gravity via the variational principle. The analysis is valid for both the traditional form of $F(T)$ gravity theory as well as the more recently introduced Lorentz covariant theory of Kr\v{s}\v{s}\'ak and Saridakis. We find that the general junction conditions derived, when applied to simple cases such as highly symmetric static or time dependent geometries (such as spherical symmetry) imply both the Synge junction conditions as well as the Israel-Sen-Lanczos-Darmois junction conditions of General Relativity. In more complicated scenarios the junction conditions derived do not generally imply the well-known junction conditions of General Relativity. However, the junctions conditions of de la Cruz-Dombriz, Dunsby, and S\'aez-G\'omez make up an interesting subset of this more general case.