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On the Einstein–Vlasov system with hyperbolic symmetry

Published online by Cambridge University Press:  02 May 2003

HÅKAN ANDRÉASSON ,
GERHARD REIN  and
ALAN D. RENDALL
HÅKAN ANDRÉASSON
Affiliation:
Department of Mathematics, Chalmers University of Technology, S-41296 Göteborg, Sweden. e-mail: hand@math.chalmers.se
GERHARD REIN
Affiliation:
Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Vienna, Austria. e-mail: gerhard.rein@univie.ac.at
ALAN D. RENDALL
Affiliation:
Max-Planck-Institut für Gravitationsphysik, Am Mühlenberg 1, D-14476 Golm, Germany. e-mail: rendall@aei-potsdam.mpg.de
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Abstract

It is shown that a spacetime with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry can be globally covered by compact hypersurfaces on which the mean curvature is constant and by compact hypersurfaces on which the area radius is constant. Results for the related cases of spherical and plane symmetry are reviewed and extended. The prospects of using the global time coordinates obtained in this way to investigate the global geometry of the spacetimes concerned are discussed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 134 , Issue 3 , May 2003 , pp. 529 - 549
Copyright
2003 Cambridge Philosophical Society

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