The structure of non-spacelike curves from a spacetime singularity

We investigate here the causal structure of spacetime in the vicinity of a spacetime singularity. The particle and energy emission from such ultra-dense regions forming in gravitational collapse of a massive matter cloud is governed by the nature of non-spacelike paths near the same. These trajectories are examined to show that if a null geodesic comes out from the singularity, then there exist families of future-directed non-spacelike curves which also necessarily escape from the naked singularity. The existence of such families is crucial to the physical visibility of the singularity. We do not assume any underlying symmetries for the spacetime, and earlier considerations on the nature of causal trajectories emerging from a naked singularity are generalized and clarified.