Kodama-like Vector Fields in Axisymmetric Spacetimes
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916319660605440 |
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| author | Dorau, Philipp Verch, Rainer |
| author_facet | Dorau, Philipp Verch, Rainer |
| contents | We extend the concept of the Kodama symmetry, a quasi-local time translation symmetry for dynamical spherically symmetric spacetimes, to a specific class of dynamical axisymmetric spacetimes, namely the families of Kerr-Vaidya and Kerr-Vaidya-de Sitter spacetimes. We study some geometrical properties of the asymptotically flat Kerr-Vaidya metric, such as the Brown-York mass and the Einstein tensor. Furthermore, we propose a generalization of the Kerr-Vaidya metric to an asymptotic de Sitter background. We show that for these classes of dynamical axisymmetric black hole spacetimes, there exists a timelike vector field that exhibits similar properties to the Kodama vector field in spherical symmetry. This includes the construction of a covariantly conserved current and a corresponding locally conserved charge, which in the Kerr-Vaidya case converges to the Brown-York mass in the asymptotically flat region. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18993 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kodama-like Vector Fields in Axisymmetric Spacetimes Dorau, Philipp Verch, Rainer General Relativity and Quantum Cosmology We extend the concept of the Kodama symmetry, a quasi-local time translation symmetry for dynamical spherically symmetric spacetimes, to a specific class of dynamical axisymmetric spacetimes, namely the families of Kerr-Vaidya and Kerr-Vaidya-de Sitter spacetimes. We study some geometrical properties of the asymptotically flat Kerr-Vaidya metric, such as the Brown-York mass and the Einstein tensor. Furthermore, we propose a generalization of the Kerr-Vaidya metric to an asymptotic de Sitter background. We show that for these classes of dynamical axisymmetric black hole spacetimes, there exists a timelike vector field that exhibits similar properties to the Kodama vector field in spherical symmetry. This includes the construction of a covariantly conserved current and a corresponding locally conserved charge, which in the Kerr-Vaidya case converges to the Brown-York mass in the asymptotically flat region. |
| title | Kodama-like Vector Fields in Axisymmetric Spacetimes |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2402.18993 |