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

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

2004-05-07

arxiv.org/abs/gr-qc/0405039v2

J.Hyperbol.Diff.Equat. 1 (2004) 691-724

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

33 pages, typos corrected, second conclusion of theorem 4.5 and remark 4.6 removed

Scientific paper

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.

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