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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/2408.03701 |
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| _version_ | 1866911604758544384 |
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| author | Kozaki, Hiroshi Ishihara, Hideki Koike, Tatsuhiko Morisawa, Yoshiyuki |
| author_facet | Kozaki, Hiroshi Ishihara, Hideki Koike, Tatsuhiko Morisawa, Yoshiyuki |
| contents | We construct a four-dimensional spacetime using a three-dimensional contact manifold equipped with a degenerate metric. The degenerate metric is set to be compatible with the contact structure. The compatibility condition is defined in this paper. Our construction yields a Ricci tensor of a particularly simple form, which leads to a solution of the Einstein equation with a null dust and cosmic strings. The solution includes two arbitrary functions: the energy density of the null dust and the number density of the cosmic strings. When there exist the cosmic strings, the spacetime is of Petrov type D. Otherwise, the spacetime is conformally flat. For some simple matter densities, we examine the Einstein equation in detail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03701 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spacetime constructed from a contact manifold with a degenerate metric Kozaki, Hiroshi Ishihara, Hideki Koike, Tatsuhiko Morisawa, Yoshiyuki General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics We construct a four-dimensional spacetime using a three-dimensional contact manifold equipped with a degenerate metric. The degenerate metric is set to be compatible with the contact structure. The compatibility condition is defined in this paper. Our construction yields a Ricci tensor of a particularly simple form, which leads to a solution of the Einstein equation with a null dust and cosmic strings. The solution includes two arbitrary functions: the energy density of the null dust and the number density of the cosmic strings. When there exist the cosmic strings, the spacetime is of Petrov type D. Otherwise, the spacetime is conformally flat. For some simple matter densities, we examine the Einstein equation in detail. |
| title | Spacetime constructed from a contact manifold with a degenerate metric |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2408.03701 |