Inevitability of shell crossing in the gravitational collapse of weakly charged dust spheres.

Abstract

It is shown here that shell crossing is inevitable in the gravitational collapse of weakly charged (\ensuremath{\Vert}charge density\ensuremath{\Vert}) dust spheres. That is, all the dust shells in the central part of the dust cloud are subject to shell crossing before they reach the stage of maximal contraction. This shell crossing, which is accompanied by a density singularity, indicates the breakdown of the dust model there. Most previous analyses of the gravitational collapse and gravitational bounce of charged dust spheres were based on the ``free-surface approach''---the assumption that the surface of the dust sphere moves like a test particle in Reissner-Nordstr\om spacetime. Because of the occurrence of shell crossing, the free-surface approach cannot be applied to the late stages of evolution. This makes it difficult to analyze, in general, what will be the final stage in the gravitational collapse of charged dust. However, for idealized models, in which the dust interior is considered to be self-similar and the shells are considered to collide inelastically, the shell crossing is shown to have a very significant effect on the causal structure: It completely prevents the gravitational bounce. This result, the inevitability of shell crossing (and its potential to affect drastically the causal structure), is in remarkable contrast to common ideas about charged-dust collapse.