Non-radial null geodesics in spherical dust collapse

TL;DR

This paper investigates the conditions under which non-radial null geodesics can emanate from a singularity in spherical dust collapse, demonstrating their existence is tied to radial geodesics, thus supporting the robustness of earlier findings.

Contribution

It establishes necessary and sufficient conditions for the existence of non-radial null geodesics from a singularity, linking their existence to radial geodesics in spherical dust collapse.

Findings

Non-radial null geodesics exist if and only if radial null geodesics exist.

Results hold for initial data of class C^3.

Supports the robustness of previous radial geodesic results.

Abstract

The issue of the local visibility of the shell-focussing singularity in marginally bound spherical dust collapse is considered from the point of view of the existence of future-directed null geodesics with angular momentum which emanate from the singularity. The initial data (i.e. the initial density profile) at the onset of collapse is taken to be of class $C^3$. Simple necessary and sufficient conditions for the existence of a naked singularity are derived in terms of the data. It is shown that there exist future-directed non-radial null geodesics emanating from the singularity if and only if there exist future-directed radial null geodesics emanating from the singularity. This result can be interpreted as indicating the robustness of previous results on radial geodesics, with respect to the presence of angular momentum.