Maximal and Willmore Null Hypersurfaces in Generalized Robertson-Walker Spacetimes

Abstract

We establish after some technical results a characterization of maximal null hypersurfaces in terms of a constant mean curvature screen foliation (in the slices) induced by the Chen's vector field. Thereafter, bounds are provided for both the squared norm of the (screen) shape operator for non totally geodesic maximal null hypersurfaces and the scalar curvature of the fiber. In terms of the scalar curvature of the fiber and the warping function, we establish necessary and sufficient conditions for Null Convergence Condition (NCC) to be satisfied in which case we prove that there are no non totally geodesic maximal null hypersurfaces. A generic example consisting of graphs of functions defined on the fiber is given to support our results. Finally, we provide lower bounds for the extrinsic scalar curvature and give a characterization result for Willmore null hypersurfaces in generalized Robertson-Walker spacetimes.