New Calabi–Bernstein type results in weighted generalized Robertson–Walker spacetimes

We apply suitable generalized maximum principles in order to obtain new Calabi–Bernstein’s type results concerning complete spacelike hypersurfaces immersed in a weighted generalized Robertson–Walker spacetime. Assuming a natural comparison inequality between the weighted mean curvatures of the hypersurface and those of the slices of the timelike bounded region where the hypersurface is supposed to be contained, we get sufficient conditions which guarantee that such a hypersurface must be a slice. Furthermore, we also treat the case when the ambient spacetime is static.