Shell-crossings in Gravitational Collapse

Abstract

While studying the continual gravitational collapse of a massive matter cloud in general relativity towards examining collapse final states, an important issue is that of whether shell-crossing singularities can develop as the collapse evolves. We examine this here to show that for any spherically symmetric collapse in general, 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 final genuine shell-focusing singularity of collapse where the physical radius of the matter cloud shrinks to a vanishing value, we can always consider without any loss of generality a collapsing ball of a finite comoving radius in which there are no shell-crossings taking place. This clarifies an important point for gravitational collapse studies.

4 pages, typos corrected and references added

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• Can we observationally test the weak cosmic censorship conjecture?
• Gravitational Collapse of Baryonic and Dark matter
• Compact objects from gravitational collapse: an analytical toy model
• All black holes in Lemaitre-Tolman-Bondi inhomogeneous dust collapse
• Tipler Naked Singularities in $N$ Dimensions
• Qualitative analysis of collapsing isotropic fluid spacetimes
• Singularity Avoidance in Gravitational Collapse of an Inhomogeneous Fluid in Rastall Gravity
• Infeasibility of Graviton Detection as Cosmic Censorship