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

摘要

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.