Gauge-invariant perturbation theory on the Schwarzschild background spacetime Part II: -- Even-mode perturbations
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866911214621163520 |
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| author | Nakamura, Kouji |
| author_facet | Nakamura, Kouji |
| contents | This is the Part II paper of our series of papers on a gauge-invariant perturbation theory on the Schwarzschild background spacetime. After reviewing our general framework of the gauge-invariant perturbation theory and the proposal on the gauge-invariant treatments for $l=0,1$ mode perturbations on the Schwarzschild background spacetime in the Part I paper [K.~Nakamura, arXiv:2110.13508 [gr-qc]], we examine the linearized Einstein equations for even-mode perturbations. We discuss the strategy to solve the linearized Einstein equations for these even-mode perturbations including $l=0,1$ modes. Furthermore, we explicitly derive the $l=0,1$ mode solutions to the linearized Einstein equations in both the vacuum and the non-vacuum cases. We show that the solutions for $l=0$ mode perturbations includes the additional Schwarzschild mass parameter perturbation, which is physically reasonable. Then, we conclude that our proposal of the resolution of the $l=0,1$-mode problem is physically reasonable due to the realization of the additional Schwarzschild mass parameter perturbation and the Kerr parameter perturbation in the Part I paper. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2110_13512 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Gauge-invariant perturbation theory on the Schwarzschild background spacetime Part II: -- Even-mode perturbations Nakamura, Kouji General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena High Energy Physics - Theory Mathematical Physics This is the Part II paper of our series of papers on a gauge-invariant perturbation theory on the Schwarzschild background spacetime. After reviewing our general framework of the gauge-invariant perturbation theory and the proposal on the gauge-invariant treatments for $l=0,1$ mode perturbations on the Schwarzschild background spacetime in the Part I paper [K.~Nakamura, arXiv:2110.13508 [gr-qc]], we examine the linearized Einstein equations for even-mode perturbations. We discuss the strategy to solve the linearized Einstein equations for these even-mode perturbations including $l=0,1$ modes. Furthermore, we explicitly derive the $l=0,1$ mode solutions to the linearized Einstein equations in both the vacuum and the non-vacuum cases. We show that the solutions for $l=0$ mode perturbations includes the additional Schwarzschild mass parameter perturbation, which is physically reasonable. Then, we conclude that our proposal of the resolution of the $l=0,1$-mode problem is physically reasonable due to the realization of the additional Schwarzschild mass parameter perturbation and the Kerr parameter perturbation in the Part I paper. |
| title | Gauge-invariant perturbation theory on the Schwarzschild background spacetime Part II: -- Even-mode perturbations |
| topic | General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2110.13512 |