The structure of non-spacelike geodesics in dust collapse

TL;DR

This paper analyzes the behavior of non-spacelike geodesics in dust collapse models to understand the causal structure of spacetime, especially in cases with naked singularities, revealing similarities in geodesic behavior near singularities.

Contribution

It provides a detailed analysis of geodesic families in dust collapse models, highlighting their behavior near naked singularities and the limiting similarities across different geodesic types.

Findings

Geodesic families differ based on initial data in naked singularity cases.

Limiting behavior of geodesics is similar across different types near the singularity.

Insights into the causal structure of dust collapse spacetimes.

Abstract

We study here the behaviour of non-spacelike geodesics in dust collapse models in order to understand the casual structure of the spacetime. The geodesic families coming out, when the singularity is naked, corresponding to different initial data are worked out and analyzed. We also bring out the similarity of the limiting behaviour for different types of geodesics in the limit of approach to the singularity.