Codimension two spacelike submanifolds into null hypersurfaces of generalized Robertson–Walker spacetimes

Abstract

Abstract We study codimension two spacelike submanifolds contained into a general class of null hypersurfaces in generalized Robertson–Walker spacetimes, refer to as nullcones. In particular we analyze light cones and lightlike cylinders in Lorentz–Minkowski spacetime, as well as nullcones in de Sitter spacetime. We give conditions on a radial coordinate that guarantee that such a spacelike submanifold is conformally diffeomorphic to the hyperbolic space, a round cylinder or a sphere; respectively. We also provide some non-existence results for weakly trapped submanifolds.