Uniqueness of Noncompact Spacelike Hypersurfaces of Constant Mean Curvature in Generalized RobertsonWalker Spacetimes
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چکیده
On any spacelike hypersurface of constant mean curvature of a Generalized Robertson–Walker spacetime, the hyperbolic angle y between the future-pointing unit normal vector field and the universal time axis is considered. It is assumed that y 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 y, and also assuming certain matter energy conditions hold just at this point, is proved. Mathematics Subject Classifications (2000). Primary 53C42; Secondary 53C50, 53C80.
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تاریخ انتشار 2002