A Connection of Apparent Horizon and Naked Singularities in Spherical Dust Collapse

TL;DR

This paper explores the link between apparent horizons and naked singularities in spherical dust collapse, analyzing null geodesics and Penrose diagrams to understand conditions leading to naked singularities.

Contribution

It establishes a connection between null geodesic behavior on the apparent horizon and the occurrence of naked singularities, with implications for general gravitational collapse scenarios.

Findings

Outgoing null geodesic behavior distinguishes naked from covered singularities.

Penrose diagrams differ significantly between naked and covered collapse cases.

The relationship may be applicable to broader gravitational collapse models.

Abstract

We show that the behaviour of outgoing radial null geodesic congruence on the apparent horizon is related to the property of nakedness in spherical dust collapse justifying the difference between the Penrose diagrams in the naked and covered dust collapse scenarios. We provide arguments suggesting that the relationship could be generally valid.