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

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.