Spacelike hypersurfaces with constant rth mean curvature in steady state type spacetimes

Abstract

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 \({-\mathbb{R} \times_{e^t} M^n}\). 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 spacelike slices \({\{t\} \times M^n}\). Afterwards, we apply such characterization results to study the uniqueness of complete spacelike hypersurfaces with one end in such a ambient space.