Rigidity of complete spacelike hypersurfaces in spatially weighted generalized Robertson–Walker spacetimes

Abstract

Our purpose in this paper is to apply some maximum principles in order to study the rigidity of complete spacelike hypersurfaces immersed in a spatially weighted generalized Robertson–Walker (GRW) spacetime, which is supposed to obey the so called strong null convergence condition. Under natural constraints on the weight function and on the f-mean curvature, we establish sufficient conditions to guarantee that such a hypersurface must be a slice of the ambient spacetime. In this setting, we also obtain new Calabi–Bernstein type results concerning entire graphs in a spatially weighted GRW spacetime.