Geometriae Dedicata

, Volume 93, Issue 1, pp 1–10 | Cite as

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

  • José M. Latorre
  • Alfonso Romero
Dedication

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.

Bochner–Lichnerowicz's formula Constant mean curvature GRW spacetime spacelike hypersurface 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • José M. Latorre
    • 1
  • Alfonso Romero
    • 1
  1. 1.Departamento de Geometría y Topología, Facultad de CienciasUniversidad de GranadaGranadaSpain

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