Explicit Kundt type II and N solutions as gravitational waves in various type D and O universes

A particular yet large class of non-diverging solutions which admits a cosmological constant, electromagnetic field, pure radiation and/or general non-null matter component is explicitly presented. These spacetimes represent exact gravitational waves of arbitrary profiles which propagate in background universes such as Minkowski, conformally flat (anti-)de Sitter, Edgar–Ludwig, Bertotti–Robinson and type D (anti-)Nariai or Plebanski–Hacyan spaces, and their generalizations. All possibilities are discussed and interpreted using a unifying simple metric form. Sandwich and impulsive waves propagating in the above background spaces with different geometries and matter content can easily be constructed. New solutions are identified, e.g. type D pure radiation or explicit type II electrovacuum waves in the (anti-)Nariai universe. It is also shown that, in general, there are no conformally flat Einstein–Maxwell fields with a non-vanishing cosmological constant.