Future asymptotic behavior of three-dimensional spacetimes with massive particles

Abstract

We consider non-vacuum initial data for the three-dimensional Einstein equations coupled to Vlasov matter composed of massive particles, on an arbitrary compact Cauchy hypersurface without boundary. We show that conservation of the total mass implies future completeness of the corresponding maximal development in the isotropic case, independent of the topology. This behavior is fundamentally different from the vacuum case and also from the same model in higher dimensions. In particular, we find that a positive mass of particles in three dimensions avoids recollapse of the spatial geometry. Finally, we construct similar solutions for the Einstein-dust system and describe to what extent the construction fails for massless matter models.