  Any compact spacelike hypersurface immersed in a doubly warped product
spacetime $I{}_{h} \times_{\rho} \mathbb{P}$ with nondecreasing warping factor
$\rho$ must be a spacelike slice, provided that the mean curvature satisfies
$H\geq\rho'/h\rho$ 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.
