Naked singularities in dust collapse as an existence problem for O.D.E. at a singular point

TL;DR

This paper formulates the end state of dust cloud collapse as an existence problem for a differential equation near a singularity, providing rigorous results for all initial data scenarios.

Contribution

It introduces a novel mathematical framework to analyze naked singularities in dust collapse through differential equations.

Findings

Rigorous existence results for radial null geodesics near singularities

Complete coverage of initial data spectrum

Insights into conditions for naked singularity formation

Abstract

The final state of the gravitational collapse of a marginally bound dust cloud is formulated in terms of an existence problem for the non-linear differential equation governing radial null geodesics near the singular point. Rigorous results are proved, covering the complete spectrum of the possible initial data.