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

Tegankong, David; Noutchegueme, Norbert; Rendall, Alan D.

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

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Rendall, Alan D.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Tegankong, D., Noutchegueme, N., & Rendall, A. D. (2004). Local existence and continuation criteria for solutions of the Einstein-Vlasov-scalar field system with surface symmetry. Journal of Hyperbolic Differential Equations, 1: 691. Retrieved from http://www.worldscinet.com/jhde/jhde.shtml.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-5154-C

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.