A Note on Spacelike Hypersurfaces and Timelike Conformal Vectors

Any compact spacelike hypersurface immersed in a doubly warped product spacetime I x P with nondecreasing warping factor ρ must be a spacelike slice, provided that the mean curvature satisfies H ≥ ρ′∕hρ everywhere on the hypersurface. The conclusion also holds, under suitable assumptions on the immersion, when the hypersurface is complete and noncompact. A similar rigidity property is shown for compact hypersurfaces in spacetimes carrying a conformal, strictly expanding, timelike vector field.