Strong curvature naked singularities in spherically symmetric perfect fluid collapse
Karim Mosani, Dipanjan Dey, Pankaj S. Joshi
Abstract
We investigate here the locally naked singularity formed due to a spherically symmetric inhomogeneous collapsing cloud having nonzero isotropic pressure, in terms of its strength. A sufficient condition provided by Clarke and Krolak for it to be Tipler strong has been used to restrict the parameters that represent the nonlinear relation between the physical radius and the radial coordinate of the outgoing radial null geodesic at the singular center. Studying an end state of a collapsing cloud requires information about the dynamics of collapse, which is unknown in a general scenario. Hence we study small perturbations to the mass profile for inhomogeneous dust, which is possible using the formalism developed here. This perturbed mass profile, in turn, gives rise to nonzero pressure. We show the existence of a nonzero measure set of initial data giving rise to such strong curvature naked singularity.