On the completeness of gravitational pp-wave spacetimes: A counterexample to the {Ehlers--Kundt} conjecture

This paper concerns the geometry of gravitational pp-wave spacetimes. We give a counterexample to the Ehlers--Kundt conjecture. In fact, we show that geodesic completeness is generic, in the sense of Baire category, among gravitational pp-waves. We also define a concept of ``universal pp-wave'', i.e