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

TL;DR

This paper investigates the geometry of codimension two spacelike submanifolds within null hypersurfaces of generalized Robertson-Walker spacetimes, providing conditions for conformal diffeomorphisms and non-existence results for certain trapped submanifolds.

Contribution

It introduces new geometric conditions for spacelike submanifolds in null hypersurfaces of generalized Robertson-Walker spacetimes and explores their conformal properties and existence constraints.

Findings

Conditions for submanifolds to be conformally diffeomorphic to hyperbolic space, cylinder, or sphere.

Analysis of light cones and lightlike cylinders in Lorentz-Minkowski spacetime.

Non-existence results for weakly trapped submanifolds.

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 null cones 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 a sphere; respectively. We also provide some non-existence results for weakly trapped submanifolds.