Global existence and future asymptotic behaviour for solutions of the Einstein-Vlasov-scalar field system with surface symmetry
David Tegankong
Abstract
We prove in the cases of plane and hyperbolic symmetries a global in time existence result in the future for comological 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. The spacetime is future geodesically complete in the special case of plane symmetry with only a scalar field. Causal geodesics are also shown to be future complete for homogeneous solutions of the Einstein-Vlasov-scalar field system with plane and hyperbolic symmetry.
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