Initial data and spherical dust collapse - art. no. 044001

By considering families of radial null geodesics, we study the subsets of i nitial data that lead to naked singularities and black holes in inhomogeneo us spherical dust collapse. We introduce the notion of central homogeneity for spherical dust collapse and prove that, for the occurrence of naked sin gularities, the initial data set must in general he centrally homogeneous. Even though mathematically this indicates that naked singularities are in g eneral unstable, we show that centrally inhomogeneous perturbations in the initial data are not physically reasonable. This provides an example of the fact that instability in this context deduced with respect to general pert urbations can become stabilized once the class of perturbations is restrict ed to be physical, This is a potentially important point to bear in mind in the general debates regarding the generic presence of naked singularities in gravitational collapse and in more general debates concerning the questi ons of genericity in general relativity.