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A generalization of the concept of constant mean curvature and canonical time

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Abstract

Some compact spaces of achronal hypersurfaces are constructed in various types of space-time. A variational principle is introduced on these spaces, smooth extremals of which are spacelike hypersurfaces of constant mean curvature. The integrand of the variational principle is shown to be upper semicontinuous and the direct methods of the calculus of variations are applied to obtain aC 0 extremal, which is defined to be a spacelike hypersurface of generalized constant mean curvature. The family of such hypersurfaces generated by altering the value of the mean curvature is discussed and the mean curvature itself is shown to have many of the properties of a canonical time coordinate.

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Author notes

  1. Andrew John Goddard

    Present address: The Department of Mathematics, The University, DD1 4HN, Dundee, UK

Authors and Affiliations

  1. The Mathematical Institute, Oxford, England

    Andrew John Goddard

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  1. Andrew John Goddard
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Goddard, A.J. A generalization of the concept of constant mean curvature and canonical time. Gen Relat Gravit 8, 525–537 (1977). https://doi.org/10.1007/BF00762636

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  • DOI: https://doi.org/10.1007/BF00762636

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