The genericity of naked singularities in gravitational collapse

We investigate here the spectrum of gravitational collapse endstates when arbitrarily small pressure perturbations are introduced in the classic black hole formation scenario as described by Oppenheimer, Snyder and Datt (OSD)[1]. The existence of classes of pressure perturbations is shown explicitly, which has the property that injecting any smallest pressure changes the final fate of the dynamical collapse from a black hole to a naked singularity. It is therefore seen that any smallest neighborhood of the OSD model, in the space of initial data, contains collapse evolutions that go to a naked singularity outcome. This gives an intriguing insight on the genericity of naked singularity formation in gravitational collapse evolutions, and towards any possible formulation of the cosmic censorship hypothesis which remains one of the most important unresolved problems in gravitation theory today.