Some exact models of inhomogeneous dust collapse

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Abstract
Three classes of irrotational-dust-collapse models with high symmetries are studied. The interior collapsing solution is joined smoothly onto an exterior static vacuum. The spherical model is just a generalization of the Oppenheimer-Snyder model. A black hole is formed in this case. The plane-symmetric model turns out to either have negative gravitating mass and bounce, never reaching the singularity, or have no static exterior. In the latter case all we get for the exterior is a Kasner universe. In the cylindrical case, however, we succeed in constructing a model that, starting with initially regular conditions, collapses into the naked singularity of an external static field.