All non-expanding gravitational waves in -dimensional (anti-)de Sitter space
arXiv:2408.15638 · doi:10.1103/PhysRevD.110.124032
Abstract
We present a complete, theory-independent classification of -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 -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 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.
arXiv comment29 pages, 1 table. v2: typos fixed, minor improvements to the text
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