The final fate of spherical inhomogeneous dust collapse II: Initial data and causal structure of singularity

TL;DR

This paper investigates how initial density and velocity distributions influence the final outcome and causal structure of singularities in spherical dust collapse, analyzing apparent horizons, geodesics, and stability aspects.

Contribution

It provides a detailed analysis of the causal structure of singularities based on initial data, extending previous results and exploring stability and geodesic behavior.

Findings

Initial data significantly affect singularity outcomes.

Apparent horizon evolution reveals causal structure.

Geodesic analysis offers insights into singularity nature.

Abstract

Further to results in [9], pointing out the role of initial density and velocity distributions towards determining the final outcome of spherical dust collapse, the causal structure of singularity is examined here in terms of evolution of the apparent horizon. We also bring out several related features which throw some useful light towards understanding the nature of this singularity, including the behaviour of geodesic families coming out and some aspects related to the stability of singularity.