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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2408.15638 |
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| _version_ | 1866910768041033728 |
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| author | Ortaggio, Marcello Voldřich, Jakub Barrientos, José |
| author_facet | Ortaggio, Marcello Voldřich, Jakub Barrientos, José |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15638 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | All non-expanding gravitational waves in $D$-dimensional (anti-)de Sitter space Ortaggio, Marcello Voldřich, Jakub Barrientos, José General Relativity and Quantum Cosmology High Energy Physics - Theory 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. |
| title | All non-expanding gravitational waves in $D$-dimensional (anti-)de Sitter space |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2408.15638 |