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Communications in Mathematical Physics

, Volume 54, Issue 3, pp 279–282 | Cite as

Foliations of space-times by spacelike hypersurfaces of constant mean curvature

  • A. J. Goddard
Article

Abstract

The foliations under discussion are of two different types, although in each case the leaves areC2 spacelike hypersurfaces of constant mean curvature. For manifolds, such as that of the Friedmann universe with closed spatial sections, which are topologicallyI×S3,I an open interval, the leaves will be spacelike hypersurfaces without boundary and the foliation will fill the manifold. In the case of the domain of dependence of a spacelike hypersurface,S, with boundaryB, the leaves will be spacelike hypersurfaces with boundary,B, and the foliation will fillD(S).

It is shown that a local energy condition ensures that the constant mean curvature increases monotonically with time through such foliations and that, in the case of a foliation whose leaves are spacelike hypersurfaces without boundary in a manifold where this energy condition is satisfied globally, the foliation is unique.

Keywords

Neural Network Manifold Statistical Physic Complex System Energy Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Eisenhart, L.: Riemannian Geometry. Princeton, NJ 1925Google Scholar
  2. 2.
    Hawking, S., Ellis, G.: The large scale structure of space time. C.U.P. 1973Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • A. J. Goddard
    • 1
  1. 1.The Department of MathematicsThe UniversityDundeeUK

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