Completeness of general pp-wave spacetimes and their impulsive limit

Abstract

We investigate geodesic completeness in the full family of pp-wave or Brinkmann spacetimes in their extended as well as in their impulsive form. This class of geometries contains the recently studied gyratonic pp-waves, modelling the exterior field of a spinning beam of null particles, as well as NPWs, which generalise classical pp-waves by allowing for a general wave surface. The problem of geodesic completeness reduces to the question of completeness of trajectories on a Riemannian manifold under an external force field. Building upon respective recent results we derive completeness criteria in terms of the spatial asymptotics of the profile function in the extended case. In the impulsive case we use a fixed point argument to show that irrespective of the behaviour of the profile function all geometries in the class are complete.

arXiv comment26 pages, 3 figures

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Cited by in corpus (6)

• Variations of the Energy of Free Particles in the pp-Wave Spacetimes
• The memory effect in impulsive plane waves: comments, corrections, clarifications
• Penrose junction conditions extended: impulsive waves with gyratons
• The Work-Energy Relation for Particles on Geodesics in the pp-Wave Spacetimes
• Ehlers-Kundt Conjecture about Gravitational Waves and Dynamical Systems
• Geodesics in nonexpanding impulsive gravitational waves with $\Lambda$, II