Non-radial null geodesics in spherical dust collapse

The issue of the local visibility of the shell-focusing singularity in marg inally bound spherical dust collapse is considered from the point of view o f the existence of future-directed null geodesics with angular momentum whi ch 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 nece ssary and sufficient conditions for the existence of a naked singularity ar e derived in terms of the data. It is shown that there exist future-directe d non-radial null geodesics emanating from the singularity if and only if t here exist future-directed radial null geodesics emanating from the singula rity. This result can be interpreted as indicating the robustness of previo us results on radial geodesics, with respect to the presence of angular mom entum.