On the cylindrically symmetric Einstein-Vlasov system

Abstract: For the cylindrically symmetric ''asymptotically flat'' Einstein equations in the case of electro-vacuum it is known that solutions exist globally and even that this class of spacetimes are causally geodesically complete. Hence the strong cosmic censorship holds for this class. An interesting question is whether these results can be generalized to include spacetimes with matter, e.g. collisionless matter described by the Vlasov equation. Thisresult is known to hold for spherically symmetric asymptotically flat solutions with small initial data. For arbitrary (in size) data it has been shown that if a singularity occurs the first one occurs at the origin. In this paper we begin the study of the question of global existence for the cylindrically symmetric Einstein-Vlasov system and we show that if a singularity occurs at all, the first one occurs at the axis of symmetry