Elastic thick shells in general relativity

It is shown that exact spherically symmetric solutions to Einstein's field equations exist such that, over an open region of the spacetime, they are singularity free, satisfy the dominant energy condition, represent elastic matter with a well-defined constitutive function, and are such that elastic perturbations propagate causally. Two toy models are then built up in which a thick elastic, spherically symmetric shell with the above properties, separates two Robertson-Walker regions corresponding to different values of the curvature k in the first model and to the same value of k in the second model. The junction conditions (continuity of the first and second fundamental forms) are shown to be exactly satisfied across the corresponding matching spherical surfaces.