Gravitational Multipoles in Five Dimensions
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910394716520448 |
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| author | Heynen, Jef Mayerson, Daniel R. |
| author_facet | Heynen, Jef Mayerson, Daniel R. |
| contents | We define gravitational mass and current multipoles for five-dimensional, stationary, and asymptotically flat vacuum metrics. We do this by generalizing Thorne's asymptotically Cartesian and mass-centered (ACMC) coordinate formalism to five dimensions, and prove that the multipoles defined in this way are unambiguously well-defined. Further, these two towers of multipole tensors, in the case of biaxial symmetry, reduce to a tower of mass multipoles $M_\ell$, and two separate towers of current or angular momentum multipoles $S^{(1)}_\ell, S^{(2)}_\ell$. We apply our formalism to a few examples, in particular Myers-Perry black holes, black rings, and smooth multicentered geometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04352 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gravitational Multipoles in Five Dimensions Heynen, Jef Mayerson, Daniel R. General Relativity and Quantum Cosmology High Energy Physics - Theory We define gravitational mass and current multipoles for five-dimensional, stationary, and asymptotically flat vacuum metrics. We do this by generalizing Thorne's asymptotically Cartesian and mass-centered (ACMC) coordinate formalism to five dimensions, and prove that the multipoles defined in this way are unambiguously well-defined. Further, these two towers of multipole tensors, in the case of biaxial symmetry, reduce to a tower of mass multipoles $M_\ell$, and two separate towers of current or angular momentum multipoles $S^{(1)}_\ell, S^{(2)}_\ell$. We apply our formalism to a few examples, in particular Myers-Perry black holes, black rings, and smooth multicentered geometries. |
| title | Gravitational Multipoles in Five Dimensions |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.04352 |