Generic naked singularities in Vaidya spacetimes

Abstract

We investigate the occurrence of naked singularities, local and global, in the incoming Vaidya spacetimes with zero initial mass. While it is well-known that these spacetimes admit locally and globally naked singularities, we demonstrate that globally naked singularities are significantly more common than is stressed in the literature, being generic in a natural topology on this collection of spacetimes. A heuristic consequence of the results is that the slow accumulation of mass is both necessary and sufficient for both types of naked singularity in these spacetimes. We demonstrate that the naked singularity, as long as it exists, always has divergent curvature (Kretschmann scalar) associated to it along emerging null curves, regardless of the form of the mass function. In particular, a consequence is that the curvature strength of the singularity cannot be smoothed away.