On the global visibility of singularity in quasi-spherical collapse

TL;DR

This paper investigates the conditions under which singularities in quasi-spherical gravitational collapse are visible locally or globally, impacting the validity of cosmic censorship hypotheses.

Contribution

It provides new criteria for the visibility of singularities in Szekeres models, including the concept of directionally naked singularities, and explores their implications for cosmic censorship.

Findings

Conditions for local versus global nakedness of singularities.

Formation criteria for black holes and naked singularities in Szekeres models.

Existence of directionally naked singularities.

Abstract

We analyze here the issue of local versus the global visibility of a singularity that forms in gravitational collapse of a dust cloud, which has important implications for the weak and strong versions of the cosmic censorship hypothesis. We find conditions as to when a singularity will be only locally naked, rather than being globally visible, thus preseving the weak censorship hypothesis. The conditions for formation of a black hole or naked singularity in the Szekeres quasi-spherical collapse models are worked out. The causal behaviour of the singularity curve is studied by examining the outgoing radial null geodesics, and the final outcome of collapse is related to the nature of the regular initial data specified on an initial hypersurface from which the collapse evolves. An interesting feature that emerges is the singularity in Szekeres spacetimes can be ``directionally naked''.