Comparing a gauge-invariant formulation and a "conventional complete gauge-fixing approach" for $l=0,1$ mode perturbations on the Schwarzschild background spacetime
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910698803560448 |
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| author | Nakamura, Kouji |
| author_facet | Nakamura, Kouji |
| contents | Comparison of the gauge-invariant formulation for $l=0,1$-mode perturbations on the Schwarzschild background spacetime proposed in [K.~Nakamura, Class. Quantum Grav. {\bf 38} (2021), 145010.] and a ``conventional complete gauge-fixing approach'' in which we use the spherical harmonic functions $Y_{lm}$ as the scalar harmonics from the starting point is discussed. Although it is often said that ``gauge-invariant formulations in general-relativistic perturbations are equivalent to complete gauge-fixing approaches,'' as the result of this comparison, we conclude that the derived solutions through the proposed gauge-invariant formulation and those through a ``conventional complete gauge-fixing approach'' are different. It is pointed out that there is a case where the boundary conditions and initial conditions are restricted in a conventional complete gauge-fixing approach. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_21375 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Comparing a gauge-invariant formulation and a "conventional complete gauge-fixing approach" for $l=0,1$ mode perturbations on the Schwarzschild background spacetime Nakamura, Kouji General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics Comparison of the gauge-invariant formulation for $l=0,1$-mode perturbations on the Schwarzschild background spacetime proposed in [K.~Nakamura, Class. Quantum Grav. {\bf 38} (2021), 145010.] and a ``conventional complete gauge-fixing approach'' in which we use the spherical harmonic functions $Y_{lm}$ as the scalar harmonics from the starting point is discussed. Although it is often said that ``gauge-invariant formulations in general-relativistic perturbations are equivalent to complete gauge-fixing approaches,'' as the result of this comparison, we conclude that the derived solutions through the proposed gauge-invariant formulation and those through a ``conventional complete gauge-fixing approach'' are different. It is pointed out that there is a case where the boundary conditions and initial conditions are restricted in a conventional complete gauge-fixing approach. |
| title | Comparing a gauge-invariant formulation and a "conventional complete gauge-fixing approach" for $l=0,1$ mode perturbations on the Schwarzschild background spacetime |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2407.21375 |