On pp-waves with lightlike parallel spinors
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908836689870848 |
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| author | Ammann, Bernd Glöckle, Jonathan Kroencke, Klaus |
| author_facet | Ammann, Bernd Glöckle, Jonathan Kroencke, Klaus |
| contents | We parametrize pp-wave spacetimes with compact codimension 2 hypersurfaces. In the vacuum case, we show that these spacetimes are locally in one-to-one correspondence with smooth curves of Riemannian Ricci-flat metrics modulo smooth curves of diffeomorphisms. We also prove that this one-to-one correspondence extends to pp-waves with prescribed null Ricci curvature. Moreover, the pp-wave spacetime carries a lightlike parallel spinor if and only if one (and hence all) of the Ricci-flat metrics carries a parallel spinor. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_14821 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On pp-waves with lightlike parallel spinors Ammann, Bernd Glöckle, Jonathan Kroencke, Klaus Differential Geometry 53C50 (Primary) 53C27, 53C25 (Secondary) We parametrize pp-wave spacetimes with compact codimension 2 hypersurfaces. In the vacuum case, we show that these spacetimes are locally in one-to-one correspondence with smooth curves of Riemannian Ricci-flat metrics modulo smooth curves of diffeomorphisms. We also prove that this one-to-one correspondence extends to pp-waves with prescribed null Ricci curvature. Moreover, the pp-wave spacetime carries a lightlike parallel spinor if and only if one (and hence all) of the Ricci-flat metrics carries a parallel spinor. |
| title | On pp-waves with lightlike parallel spinors |
| topic | Differential Geometry 53C50 (Primary) 53C27, 53C25 (Secondary) |
| url | https://arxiv.org/abs/2602.14821 |