Veiled singularities for the spherically symmetric massless Einstein-Vlasov system

TL;DR

This paper constructs asymptotically flat solutions for the spherically symmetric massless Einstein-Vlasov system, extending previous non-smooth self-similar solutions to more physically relevant models and exploring naked singularity formation.

Contribution

It develops methods to modify self-similar solutions to achieve asymptotic flatness in the Einstein-Vlasov system, advancing understanding of naked singularities in collisionless matter collapse.

Findings

Successfully constructed asymptotically flat solutions

Extended previous non-smooth solutions to physically relevant models

Provided insights into naked singularity formation

Abstract

This paper continues the investigation of the formation of naked singularities in the collapse of collisionless matter initiated in [RV]. There the existence of certain classes of non-smooth solutions of the Einstein-Vlasov system was proved. Those solutions are self-similar and hence not asymptotically flat. To obtain solutions which are more physically relevant it makes sense to attempt to cut off these solutions in a suitable way so as to make them asymptotically flat. This task, which turns out to be technically challenging, will be carried out in this paper. [RV] A. D. Rendall and J. J. L. Vel\'{a}zquez, A class of dust-like self-similar solutions of the massless Einstein-Vlasov system. Annales Henri Poincare 12, 919-964, (2011).