$\widetilde{L_r}-$finite type null hypersurfaces in generalized Robertson-Walker spacetimes

Abstract

This paper explores the $\widetilde{L_r}$-finite type null hypersurfaces within generalized Robertson-Walker spacetimes, where $\widetilde{L_r}$ stands for the linearized operator of the first variation of the $(r+1)-$th mean curvature arising from normal variations of the hypersurface equipped with its rigged Riemannian structure. We provide necessary and/or sufficient conditions characterizing $\widetilde{L_r}$-$p$-type and $\widetilde{L_r}$-null-$p$-type null hypersurfaces $(p=1,2)$, followed by various examples.