Apparent horizon and causal structure of spacetime singularities

Abstract

A major issue in general relativity and black-hole physics today is to determine the conditions when the spacetime singularities forming as end-states of gravitational collapse are visible to external observers, and when these are hidden within the event horizon of a black-hole. We show here that such a causal structure of singularity, in terms of its visibility or otherwise, is determined by the dynamics of the apparent horizon and trapped surfaces forming during collapse of massive matter clouds. It turns out that the relative timing of formation of trapped surfaces and the singularity plays a crucial role here. The dynamics of apparent horizon governs the visibility of singularity, and we characterize precise conditions here for the same for spherical collapse with a general type-I matter field. This is done in terms of the existence of outgoing null geodesic families from the central singularity. These results hold under generic initial data satisfying \(\mathcal {C}^2\) regularity and the weak energy condition.