Elastic thick shells in General Relativity

Abstract

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 $k$. The junction conditions (continuity of the first and second fundamental forms) are shown to be exactly satisfied across the corresponding matching spherical surfaces.

arXiv comment23 pages, 3 figures

References in corpus (7)

• Relativistic Elasticity
• Elastic Stars in General Relativity: II. Radial perturbations
• Elastic Stars in General Relativity: III. Stiff ultrarigid exact solutions
• Static Solutions of the Einstein Equations for Spherically Symmetric Elastic Bodies
• Elastic stars in general relativity: IV. Axial perturbations
• The static spherically symmetric body in relativistic elasticity
• General spherically symmetric elastic stars in Relativity