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Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes

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Abstract

A new technique is introduced in order to solve the following question:When is a complete spacelike hypersurface of constant mean curvature in a generalized Robertson-Walker spacetime totally umbilical and a slice? (Generalized Robertson-Walker spacetimes extend classical Robertson-Walker ones to include the cases in which the fiber has not constant sectional curvature.) First, we determine when this hypersurface must be compact. Then, all these compact hypersurfaces in (necessarily spatially closed) spacetimes are shown to be totally umbilical and, except in very exceptional cases, slices. This leads to proof of a new Bernstein-type result. The power of the introduced tools is also shown by reproving and extending several known results.

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Authors and Affiliations

  1. Departamento de Matemàticas, Universidad de Murcia, E-30100, Espinardo, Murcia, Spain

    Luis J. Alías

  2. Departamento de Geometría y Topología, Universidad de Granada, E-18071, Granada, Spain

    Alfonso Romero & Miguel Sánchez

Authors
  1. Luis J. Alías
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  2. Alfonso Romero
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  3. Miguel Sánchez
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Alías, L.J., Romero, A. & Sánchez, M. Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes. Gen Relat Gravit 27, 71–84 (1995). https://doi.org/10.1007/BF02105675

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  • DOI: https://doi.org/10.1007/BF02105675

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