Null hypersurfaces in general relativity: Intrinsic symmetries and differential invariants

G. Dautcourt

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arXiv · 2602.18499

Null hypersurfaces in general relativity: Intrinsic symmetries and differential invariants

G. Dautcourt

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Abstract

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.

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G. Dautcourt. 2026-02-17. Null hypersurfaces in general relativity: Intrinsic symmetries and differential invariants. https://arxiv.org/abs/2602.18499

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