A note on black hole and naked singularity

Abstract

Recently THORNY. (~) and LIANG (2) have independently constructed explicit models of cylindrical dust collapsing into the naked singularity (a) of an external vacuum field. There are also indications that similar models can exist even with pressure (4). Although such models may be too artificial because of their cylindrical symmetry, it seems that, at least for the moment, the possibility of gravitational collapse into a naked singularity should be considered. If both black hole and naked singularity arc going r stay, one question naturally arises: what is the dividing line between the initial physical conditions that will lead to one or the other? Before we can try to attack this extremely difficult problem it seems logical to first find out more about the intrinsic differences between singularities which are ~ hidden ~) behind event horizons (3) and those which are naked (a). In this note we briefly report some preliminary findings obtained after analyzing a large number of known exact solutions. We then propose a conjecture based on these results. True or not, we hope that further studies along the lines of this conjecture may bring about deeper insights into the nature of things. We deal exclusively with asymptotically flat (~) space-times and singularities at which curvature invariants and matter variables blow up. In maximally extended space-times there are usually more than one connected component of the singularity. So whenever we say ~ a ~ singularity it is understood that we are referring to one partitular component. In order to define invariant concepts we also limit ourselves to consider only geodesic normal singularity (5) (GNS), namely, singularity which admits a unique 3-parameter congruence of (spacelike or timelike) irrotational geodesics that strike it simultaneously. At present, singularities of most, if not all, known exact solu