Null hypersurfaces in general relativity: Intrinsic symmetries and differential invariants

This paper investigates intrinsic Killing symmetries of null hypersurfaces ${\mathcal{N}}_3$ within the framework of general relativity. To this end we consider ${\mathcal{N}}_3$ as detached from the embedding spacetime and equipped with a degenerate metric of signature (0,+,+). As geometrical tools we use a triad calculus and differential invariants. Extending prior work, we present a classification of null hypersurfaces according to groups of motion up to the fourth order. For each type certain normal forms of the metric are given, and their invariants are listed. A discussion of horizons - defined as null hypersurfaces with vanishing shear and divergence - is included.