Non-radial null geodesics in spherical dust collapse (Q2769505)

A singularity is called locally naked if in its neighborhood there are future-directed causal geodesics which emanate from the singularity. The study under review establishes that the existence of radial null geodesics emanating from the shell-focusing singularity in marginally bound spherical dust collapse is a necessary and sufficient condition for the existence of non-radial null geodesics emanating from the singularity. The result addresses the stability of the naked singularity: The insertion of angular momentum into the system, at the level of null geodesics, does not affect the outcome. This result is of importance as non-radial geodesics provide a better model of physically realistic trajectories than do radial geodesics. Future work along this line will be concerned with a qualitative approach to radial and non-radial timelike geodesics in order to achieve a unified treatment of all causal geodesics in marginally bound spherical dust collapse.