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

TL;DR

This paper presents a broad class of exact gravitational wave solutions in various background universes, including new solutions like type D pure radiation and electrovacuum waves, unifying their description with a simple metric form.

Contribution

It introduces a unifying metric form for explicit gravitational wave solutions across multiple background spacetimes, including new solutions with specific matter content.

Findings

Explicit solutions for gravitational waves in diverse backgrounds.

Identification of new type D pure radiation and electrovacuum wave solutions.

Demonstration that conformally flat Einstein-Maxwell fields with non-zero cosmological constant do not exist.

Abstract

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 are 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 (anti-)Nariai universe. It is also shown that, in general, there are no conformally flat Einstein-Maxwell fields with a non-vanishing cosmological constant.