Uniqueness of noncompact spacelike hypersurfaces of constant mean curvature in generalized Robertson walker spacetimes

On any spacelike hypersurface of constant mean curvature of a Generalized Robertson Walker spacetime, the hyperbolic angle theta between the future-pointing unit normal vector field and the universal time axis is considered. It is assumed that theta 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 theta, and also assuming certain matter energy conditions hold just at this point, is proved.