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Uniqueness of Noncompact Spacelike Hypersurfaces of Constant Mean Curvature in Generalized Robertson–Walker Spacetimes

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Abstract

On any spacelike hypersurface of constant mean curvature of a Generalized Robertson–Walker spacetime, the hyperbolic angle θ between the future-pointing unit normal vector field and the universal time axis is considered. It is assumed that θ has a local maximum. A physical consequence of this fact is that relative speeds between normal and comoving observers do not approach the speed of light near the maximum point. By using a development inspired from Bochner's well-known technique, a uniqueness result for spacelike hypersurfaces of constant mean curvature under this assumption on θ, and also assuming certain matter energy conditions hold just at this point, is proved.

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  1. Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain

    José M. Latorre & Alfonso Romero

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  1. José M. Latorre
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  2. Alfonso Romero
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Latorre, J.M., Romero, A. Uniqueness of Noncompact Spacelike Hypersurfaces of Constant Mean Curvature in Generalized Robertson–Walker Spacetimes. Geometriae Dedicata 93, 1–10 (2002). https://doi.org/10.1023/A:1020341512060

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