A regularity theorem for solutions of the spherically symmetric Vlasov-Einstein system

TL;DR

This paper extends previous work on the spherically symmetric Vlasov-Einstein system by showing that singularities, if they occur, must originate at the center, supporting cosmic censorship conjectures.

Contribution

It proves that solutions with large initial data can develop singularities only at the center, advancing understanding of the system's global behavior and singularity formation.

Findings

Singularities, if any, occur at the center of symmetry.

Solutions remain global if matter stays away from the center.

Supports the cosmic censorship conjecture for collisionless matter.

Abstract

In a previous paper two of the authors (G. R. and A. D. R.) showed that there exist global, classical solutions of the spherically symmetric Vlasov-Einstein system for small initial data. The present paper continues this investigation and allows also large initial data. It is shown that if a solution of the spherically symmetric Vlasov-Einstein system develops a singularity at all then the first singularity has to appear at the center of symmetry. The result adds weight to the conjecture that cosmic censorship holds if one replaces dust as matter model for which naked singularities do form by a collisionless gas described by the Vlasov equation. The main tool is an estimate which shows that a solution is global if all the matter remains away from the center of symmetry.