Null hypersurfaces in generalized Robertson–Walker spacetimes

We study the geometry of null hypersurfaces MM in generalized Robertson–Walker spacetimes. First we characterize such null hypersurfaces as graphs of generalized eikonal functions over the fiber and use this characterization to show that such hypersurfaces are parallel if and only if their fibers are also parallel. We further use this technique to construct several examples of null hypersurfaces in both de Sitter and anti de Sitter spaces. Then we characterize all the totally umbilical null hypersurfaces MM in a Lorentzian space form (viewed as a quadric in a semi-Euclidean ambient space) as intersections of the space form with a hyperplane. Finally we study the totally umbilical spacelike hypersurfaces of null hypersurfaces in space forms and characterize them as planar sections of MM.