New mathematical framework for spherical gravitational collapse

TL;DR

This paper introduces a new mathematical framework that characterizes when naked singularities form during spherical gravitational collapse, unifying known examples and enabling discovery of new cases.

Contribution

It formulates and proves a theorem providing necessary and sufficient conditions for naked singularity formation in spherically symmetric, non-static spacetimes, unifying existing examples and enabling new ones.

Findings

A theorem relating null geodesics to super-solutions of the geodesic equation

Unified treatment of known naked singularity examples

Discovery of new naked singularity solutions

Abstract

A theorem, giving necessary and sufficient condition for naked singularity formation in spherically symmetric non static spacetimes under hypotheses of physical acceptability, is formulated and proved. The theorem relates existence of singular null geodesics to existence of regular curves which are super-solutions of the radial null geodesic equation, and allows us to treat all the known examples of naked singularities from a unified viewpoint. New examples are also found using this approach, and perspectives are discussed.