Geometrical origin of the Kodama vector
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912011810504704 |
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| author | Kinoshita, Shunichiro |
| author_facet | Kinoshita, Shunichiro |
| contents | It has been known that warped-product spacetimes such as spherically symmetric ones admit the Kodama vector. This vector provides a locally conserved current made by contraction of the Einstein tensor, even though there is no Killing vector. In addition, a quasilocal mass, Birkhoff's theorem and various properties are closely related to the Kodama vector. Recently, it is shown that the notion of the Kodama vector can be extended to three-dimensional axisymmetric spacetimes even if the spacetimes are not warped product. This implies that warped product may not be a necessary condition for a spacetime to admit the Kodama vector. We show properties of the Kodama vector originate from the conformal Killing-Yano 2-form. In particular, the well-known spacetimes that admit the Kodama vector have a closed conformal Killing-Yano 2-form. Furthermore, we show the Kodama vector provides local conserved currents for each order of the Lovelock tensor as well as the Einstein tensor. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_16484 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometrical origin of the Kodama vector Kinoshita, Shunichiro General Relativity and Quantum Cosmology High Energy Physics - Theory It has been known that warped-product spacetimes such as spherically symmetric ones admit the Kodama vector. This vector provides a locally conserved current made by contraction of the Einstein tensor, even though there is no Killing vector. In addition, a quasilocal mass, Birkhoff's theorem and various properties are closely related to the Kodama vector. Recently, it is shown that the notion of the Kodama vector can be extended to three-dimensional axisymmetric spacetimes even if the spacetimes are not warped product. This implies that warped product may not be a necessary condition for a spacetime to admit the Kodama vector. We show properties of the Kodama vector originate from the conformal Killing-Yano 2-form. In particular, the well-known spacetimes that admit the Kodama vector have a closed conformal Killing-Yano 2-form. Furthermore, we show the Kodama vector provides local conserved currents for each order of the Lovelock tensor as well as the Einstein tensor. |
| title | Geometrical origin of the Kodama vector |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2402.16484 |