We deal with spacelike hypersurfaces immersed with some constant rth mean curvature in a steady state type spacetime, that is, a generalized Robertson–Walker spacetime of the type
. In this setting, supposing that the fiber M
n
of the ambient space has nonnegative constant sectional curvature, we establish characterization results concerning domains of the
... [Show full abstract] spacelike slices . Afterwards, we apply such characterization results to study the uniqueness of complete spacelike hypersurfaces with one end in such a ambient space.