All non-expanding gravitational waves in $D$-dimensional (anti-)de Sitter space

TL;DR

This paper classifies all non-expanding gravitational wave solutions in D-dimensional (anti-)de Sitter space, providing canonical forms and exploring their roles in various gravity theories.

Contribution

It offers a complete, theory-independent classification of Kundt spacetimes of Weyl and traceless-Ricci type N in D dimensions, including canonical forms and applications.

Findings

Identified three invariant subfamilies: Kundt, pp-, and Siklos waves.

Demonstrated these metrics coincide with non-expanding (A)dS-Kerr-Schild spacetimes.

Discussed applications in Einstein, Gauss-Bonnet, Lovelock, quadratic, and f(R) gravity.

Abstract

We present a complete, theory-independent classification of $D$-dimensional Kundt spacetimes of Weyl and traceless-Ricci type N. We show that these geometries consist of three invariantly defined subfamilies, namely (generalized) Kundt, pp- and Siklos waves, for each of which we obtain a convenient canonical form. As a byproduct, this also demonstrates that such metrics coincide with the class of non-expanding (A)dS-Kerr-Schild spacetimes. The role of these spacetimes in Einstein's gravity (including minimally coupled $p$-forms and non-linear electrodynamics) as non-expanding gravitational waves in an (anti)-de Sitter background is discussed. Furthermore, applications to extended theories such as Gauss-Bonnet, Lovelock, quadratic and $f(R)$ gravity are also briefly illustrated, as well as the overlap of the obtained metrics with universal and almost-universal spacetimes. In the appendices we additionally settle the issue of the redundancy of certain field equations for all Kundt spacetimes in a theory-independent way, and present various alternative coordinates for the spacetimes studied in the paper.