New Properties on Normalized Null Hypersurface

Abstract

Rigging technique introduced in Gutiérrez and Olea (Math Nachr 289:1219–1236, 2016) 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.