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

David Tegankong·Norbert Noutchegueme·Alan D. Rendall
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Abstract

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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David Tegankong, Norbert Noutchegueme, Alan D. Rendall. 2004-10-26. Local existence and continuation criteria for solutions of the Einstein-Vlasov-scalar field system with surface symmetry. https://arxiv.org/abs/gr-qc/0405039

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