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On the nature of initial singularities for solutions of the Einstein–Vlasov-scalar field system with surface symmetry

Published online by Cambridge University Press:  01 December 2006

D. TEGANKONG  and
A. D. RENDALL
D. TEGANKONG
Affiliation:
Department of Mathematics, ENS, University of Yaounde 1, Box 47, Yaounde, Cameroon. e-mail: dtegankong@yahoo.fr
A. D. RENDALL
Affiliation:
Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, D-14476 Golm, Germany. e-mail: rendall@aei.mpg.de
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Abstract

Global existence results in the past time direction of cosmological models with collisionless matter and a massless scalar field are presented. It is shown that the singularity is crushing and that the Kretschmann scalar diverges uniformly as the singularity is approached. In the case without Vlasov matter, the singularity is velocity dominated and the generalized Kasner exponents converge at each spatial point as the singularity is approached.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 141 , Issue 3 , November 2006 , pp. 547 - 562
Copyright
© 2006 Cambridge Philosophical Society

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