On the nature of initial singularities for solutions of the Einstein-Vlasov-scalar field system with surface symmetry

Global existence results in the past time direction of cosmological models with collisionless matter and a massless scalar field are presented. It is shown that the singularity is crushing and that the Kretschmann scalar diverges uniformly as the singularity is approached. In the case without Vlasov matter, the singularity is velocity dominated and the generalized Kasner exponents converge at each spatial point as the singularity is approached

Local existence and continuation criteria for solutions of the Einstein-Vlasov-scalar field system with surface symmetry

We prove in the cases of spherical, plane and hyperbolic symmetry a local in time existence theorem and continuation criteria for cosmological solutions of the Einstein-Vlasov-scalar field system, with the sources generated by a distribution function and a 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. In the case where the only source is a scalar field it is shown that a global existence result can be deduced from the general theorem.Comment: 33 pages, typos corrected, second conclusion of theorem 4.5 and remark 4.6 remove

Cosmological solutions of the Einstein-Vlasov-scalar field system

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 ...thesi