Intrinsic Geometry of a Null Hypersurface

TL;DR

This paper uses Cartan's method to develop invariants that classify the internal geometry of null hypersurfaces in 4D Lorentzian space-times, solving the local equivalence problem.

Contribution

It introduces a complete classification framework for null hypersurfaces using Cartan's method of equivalence, advancing geometric understanding in Lorentzian manifolds.

Findings

Constructed invariants for null hypersurfaces

Solved the local equivalence problem in 4D Lorentzian space-times

Provided a classification scheme for null hypersurface geometries

Abstract

We apply Cartan's method of equivalence to construct invariants of a given null hypersurface in a Lorentzian space-time. This enables us to fully classify the internal geometry of such surfaces and hence solve the local equivalence problem for null hypersurface structures in 4-dimensional Lorentzian space-times.