Genericity and stability of naked singularities arising in an inhomogeneous dust collapseS H GHATE, R V SARAYKAR and K D PATIL Department of Mathematics, Nagpur University Campus, Nagpur 440 010, India MS received 22 September 1998; revised 19 April 1999 Abstract:In this paper, we consider an inhomogeneous dust collapse, and extend earlier works of Jhingan, Joshi, and Singh to the case where initial density and velocity distributions are finitely differentiable functions of co-moving coordinate g . We study the occurrence of naked singularities under various conditions on the derivatives of initial density and velocity distributions in marginally as well as non-marginally bound case. We then study their stability and genericity with respect to perturbations in the initial data in an appropriate topological sense. Keywords. Generic properties; stability; naked singularity; gravitational collapse.
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