Publikace ÚTF

We investigate geodesic completeness in the full family of pp-wave (or
Brinkmann) spacetimes in their extended and impulsive forms. 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 N-fronted waves
with parallel rays, which generalize 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.