The final fate of spherical inhomogeneous dust collapse II: Initial data   and causal structure of singularity
  Further to results in [9], pointing out the role of initial density and velocity distributions towards determining the final outcome of spherical dust collapse, the causal structure of singularity is examined here in terms of evolution of the apparent horizon. We also bring out several related features which throw some useful light towards understanding the nature of this singularity, including the behaviour of geodesic families coming out and some aspects related to the stability of singularity. 
Sanjay Jhingan, P. S. Joshi and T. P. Singh