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LOCAL EXISTENCE AND CONTINUATION CRITERIA FOR SOLUTIONS OF THE EINSTEIN–VLASOV-SCALAR FIELD SYSTEM WITH SURFACE SYMMETRY

D. TEGANKONG

Department of Mathematics, Higher Teachers Training College, University of Yaounde 1, Box 47, Yaounde, Cameroon

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N. NOUTCHEGUEME

Department of Mathematics, Faculty of Sciences, University of Yaounde 1, Box 812, Yaounde, Cameroon

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, and

A. D. RENDALL

Max-Planck-Institut für Gravitationsphysik, Am Mühlenberg 1, D-14476 Golm, Germany

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https://doi.org/10.1142/S0219891604000305Cited by:11 (Source: Crossref)

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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