Sourced metric perturbations of Kerr spacetime in Lorenz gauge
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866918208431194112 |
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| author | Wardell, Barry Kavanagh, Chris Dolan, Sam R. |
| author_facet | Wardell, Barry Kavanagh, Chris Dolan, Sam R. |
| contents | We derive a formalism for solving the Lorenz gauge equations for metric perturbations of Kerr spacetime sourced by an arbitrary stress-energy tensor. The metric perturbation is obtained as a sum of differential operators acting on a set of six scalars, with two of spin-weight $\pm2$, two of spin-weight $\pm1$, and two of spin-weight $0$. We derive the sourced Teukolsky equations satisfied by these scalars, with the sources given in terms of differential operators acting on the stress-energy tensor. The method can be used to obtain both linear and higher order nonlinear metric perturbations, and it fully determines the metric perturbation up to a time integral, omitting only static contributions which must be handled separately. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12510 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sourced metric perturbations of Kerr spacetime in Lorenz gauge Wardell, Barry Kavanagh, Chris Dolan, Sam R. General Relativity and Quantum Cosmology We derive a formalism for solving the Lorenz gauge equations for metric perturbations of Kerr spacetime sourced by an arbitrary stress-energy tensor. The metric perturbation is obtained as a sum of differential operators acting on a set of six scalars, with two of spin-weight $\pm2$, two of spin-weight $\pm1$, and two of spin-weight $0$. We derive the sourced Teukolsky equations satisfied by these scalars, with the sources given in terms of differential operators acting on the stress-energy tensor. The method can be used to obtain both linear and higher order nonlinear metric perturbations, and it fully determines the metric perturbation up to a time integral, omitting only static contributions which must be handled separately. |
| title | Sourced metric perturbations of Kerr spacetime in Lorenz gauge |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2406.12510 |