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Local prescribed mean curvature foliations in cosmological spacetimes

Published online by Cambridge University Press:  02 May 2003

OLIVER HENKEL
OLIVER HENKEL
Affiliation:
Max Planck Institute for Gravitational Physics, Am Mühlenberg 1, 14476 Golm, Germany e-mail: henkel@hhi.de Present address: Fraunhofer Instituts for Communication Technology HHI, Einsteinufer 37, 10587 Berlin, Germany.
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Abstract

A theorem about local in time existence of spacelike foliations with prescribed mean curvature in cosmological spacetimes will be proved. The time function of the foliation is geometrically defined and fixes the diffeomorphism invariance inherent in general foliations of spacetimes. Moreover, in contrast to the situation of the more special constant mean curvature foliations, which play an important role in global analysis of spacetimes, this theorem overcomes the existence problem arising from topological restrictions for surfaces of constant mean curvature.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 134 , Issue 3 , May 2003 , pp. 551 - 571
Copyright
2003 Cambridge Philosophical Society

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