Conformal transformations near Naked Singularities - I

TL;DR

This paper explores how conformal transformations relate to the behavior of null geodesics near naked singularities in spherical dust collapse, providing insights into the structure of spacetime in these extreme regions.

Contribution

It demonstrates the connection between conformal transformations and the properties of naked singularities in dust collapse models, clarifying differences in Penrose diagrams.

Findings

Null geodesic behavior distinguishes naked from covered singularities.

Conformal transformations justify differences in Penrose diagrams.

Boundary behavior of null congruences relates to nakedness in collapse.

Abstract

We show that the behaviour of the outgoing radial null geodesic congruence on the boundary of the trapped region (suitably defined as a four dimensional region) is related to the property of nakedness in spherical dust collapse. The argument involves a conformal transformation which justifies the difference in the Penrose diagrams in the naked and covered dust collapse scenarios.