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