# New properties on normalized null hypersurfaces

## TL;DR

This paper advances the rigging technique for null hypersurfaces, revealing new properties and applications, including existence and completeness conditions for the induced Riemannian structures, enabling classical Riemannian methods.

## Contribution

It develops the rigging technique further by establishing new properties, existence results, and completeness conditions for the induced Riemannian structures on null hypersurfaces.

## Key findings

- Existence of rigging fields under geometric and topological constraints
- Conditions for completeness of the rigged Riemannian structure
- Enhanced applicability of Riemannian techniques to null hypersurfaces

## Abstract

Rigging technique introduced in \cite{bi0} is a convenient way to address the study of null hypersurfaces. It offers in addition the extra benefit of inducing a Riemannian structure on the null hypersurface which is used to study geometric and topological properties on it. In this paper we develop this technique showing new properties and applications. We first discuss the very existence of the rigging fields under prescribed geometric and topological constraints. We consider the completeness of the induced rigged Riemannian structure. This is potentially important because it allows to use most of the usual Riemannian techniques.