SHELL-CROSSINGS IN GRAVITATIONAL COLLAPSE

Abstract

An important issue in the study of continual gravitational collapse of a massive matter cloud in general relativity is whether shell-crossing singularities develop as the collapse evolves. We examine this here to show that for any spherically symmetric collapse in general, till arbitrarily close to the final singularity, there is always a finite neighborhood of the center in which there are no shell-crossings taking place. It follows that in order to study the visibility or otherwise of the ultra-dense region close to the final singularity of collapse where physical radius of the matter cloud shrinks to an arbitrarily small value, we can always consider without loss of generality a collapsing ball of finite comoving radius in which there are no shell-crossings.