Naked Singularity of the Vaidya-deSitter Spacetime and Cosmic Censorship Hypothesis

TL;DR

This paper studies the conditions under which a locally naked singularity can form during radiation shell collapse in an expanding Vaidya-deSitter spacetime, challenging the necessity of asymptotic flatness for such phenomena.

Contribution

It establishes that the condition for a locally naked singularity is the same in Vaidya-deSitter and asymptotically flat backgrounds, supporting the idea that asymptotic flatness is not essential for naked singularity formation.

Findings

Locally naked singularities can form in Vaidya-deSitter spacetime.

The condition for null geodesics to originate at the singularity is identical to the asymptotically flat case.

Supports the view that asymptotic observers are not crucial in Cosmic Censorship Hypothesis.

Abstract

We investigate the formation of a locally naked singularity in the collapse of radiation shells in an expanding Vaidya-deSitter background. This is achieved by considering the behaviour of non-spacelike and radial geodesics originating at the singularity. A specific condition is determined for the existence of radially outgoing, null geodesics originating at the singularity which, when this condition is satisfied, becomes locally naked. This condition turns out to be the same as that in the collapse of radiation shells in an asymptotically flat background. Therefore, we have, at least for the case considered here, established that the asymptotic flatness of the spacetime is not essential for the development of a locally naked singularity. Our result then unequivocally supports the view that no special role be given to asymptotic observers (or, for that matter, any set of observers) in the formulation of the Cosmic Censorship Hypothesis.