Screen bundles of Lorentzian manifolds and some generalisations of pp-waves

Abstract

A pp-wave is a Lorentzian manifold admitting a parallel light-like vector field and satisfying a certain curvature condition. On the basis of a new description of pp-waves we introduce generalisations of pp-waves, on one hand by allowing the vector field to be recurrent and on the other hand by weakening the curvature condition. We show how these generalisations can be expressed in terms of the screen bundle of the manifold and how they are related to the screen holonomy. While pp-waves have a trivial screen holonomy there are no restrictions on the screen holonomy of the generalised pp-waves defined by the weaker curvature condition.