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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.10535 |
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| _version_ | 1866913431350673408 |
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| author | Brozos-Vázquez, Miguel Mojón-Álvarez, Diego |
| author_facet | Brozos-Vázquez, Miguel Mojón-Álvarez, Diego |
| contents | We classify solutions of the vacuum weighted Einstein field equations on smooth metric measure spacetimes $(M,g,h\, dvol_g)$ of dimension 4, where the underlying manifold $(M,g)$ is a $pr$-wave. We use this result to provide examples of solutions with some special geometric properties.
The gradient $\nabla h$ is lightlike or spacelike. In the first case, the underlying manifold is a $pp$-wave. In the second case, the Ricci operator is nilpotent. Moreover, $2$-step nilpotent solutions are also realized on $pp$-waves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10535 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The vacuum weighted Einstein field equations on pr-waves Brozos-Vázquez, Miguel Mojón-Álvarez, Diego Differential Geometry 53B30, 53C50, 53C21 We classify solutions of the vacuum weighted Einstein field equations on smooth metric measure spacetimes $(M,g,h\, dvol_g)$ of dimension 4, where the underlying manifold $(M,g)$ is a $pr$-wave. We use this result to provide examples of solutions with some special geometric properties. The gradient $\nabla h$ is lightlike or spacelike. In the first case, the underlying manifold is a $pp$-wave. In the second case, the Ricci operator is nilpotent. Moreover, $2$-step nilpotent solutions are also realized on $pp$-waves. |
| title | The vacuum weighted Einstein field equations on pr-waves |
| topic | Differential Geometry 53B30, 53C50, 53C21 |
| url | https://arxiv.org/abs/2407.10535 |