The structure of non-spacelike geodesics in dust collapse
  We study here the behaviour of non-spacelike geodesics in dust collapse models in order to understand the casual structure of the spacetime. The geodesic families coming out, when the singularity is naked, corresponding to different initial data are worked out and analyzed. We also bring out the similarity of the limiting behaviour for different types of geodesics in the limit of approach to the singularity. 
S. S. Deshingkar and P. S. Joshi