Cosmological solutions of the Einstein-Vlasov-scalar field system

Abstract

The aim of this thesis is to obtain as much information as possible, about global solutions of the Cauchy problem for the Einstein-Vlasov-scalar field system with spherical, plane and hyberbolic symmetries written in areal coordinates. The sources of this system are generated by both a distribution function and a linear scalar field subject to the Vlasov and wave equations respectively. This system describes the evolution of self-gravitating collisionless matter and scalar waves within the context of general relativity. We consider the cosmological case. That is spacetimes possess a compact Cauchy hypersurface and then, data are given on a compact 3-manifold. We extend the local-in-time results obtained by G. Rein for the Einstein-Vlasov system with collisionless matter alone. This extension concerns pointwise estimates for hyperbolic equations by the method of characteristics. This means that the system is transformed to a system of ordinary differential equations which are integrated along characteristics ...