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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2023
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| Accès en ligne: | https://arxiv.org/abs/2306.17847 |
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| _version_ | 1866909241799868416 |
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| author | Spiers, Andrew Pound, Adam Wardell, Barry |
| author_facet | Spiers, Andrew Pound, Adam Wardell, Barry |
| contents | High-accuracy gravitational-wave modeling demands going beyond linear, first-order perturbation theory. Particularly motivated by the need for second-order perturbative models of extreme-mass-ratio inspirals and black hole ringdowns, we present practical spherical-harmonic decompositions of the Einstein equation, Regge-Wheeler-Zerilli equations, and Teukolsky equation at second perturbative order in a Schwarzschild background. Our formulations are covariant on the $t$--$r$ plane and on the two-sphere, and we express the field equations in terms of gauge-invariant metric perturbations. In a companion Mathematica package, PerturbationEquations, we provide these invariant formulas as well as the analogous formulas in terms of raw, gauge-dependent metric perturbations. Our decomposition of the second-order Einstein equation, when specialized to the Lorenz gauge, was a key ingredient in recent second-order self-force calculations [Phys. Rev. Lett. 124, 021101 (2020); ibid. 127, 151102 (2021); ibid. 130, 241402 (2023)]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_17847 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Second-order perturbations of the Schwarzschild spacetime: practical, covariant and gauge-invariant formalisms Spiers, Andrew Pound, Adam Wardell, Barry General Relativity and Quantum Cosmology High-accuracy gravitational-wave modeling demands going beyond linear, first-order perturbation theory. Particularly motivated by the need for second-order perturbative models of extreme-mass-ratio inspirals and black hole ringdowns, we present practical spherical-harmonic decompositions of the Einstein equation, Regge-Wheeler-Zerilli equations, and Teukolsky equation at second perturbative order in a Schwarzschild background. Our formulations are covariant on the $t$--$r$ plane and on the two-sphere, and we express the field equations in terms of gauge-invariant metric perturbations. In a companion Mathematica package, PerturbationEquations, we provide these invariant formulas as well as the analogous formulas in terms of raw, gauge-dependent metric perturbations. Our decomposition of the second-order Einstein equation, when specialized to the Lorenz gauge, was a key ingredient in recent second-order self-force calculations [Phys. Rev. Lett. 124, 021101 (2020); ibid. 127, 151102 (2021); ibid. 130, 241402 (2023)]. |
| title | Second-order perturbations of the Schwarzschild spacetime: practical, covariant and gauge-invariant formalisms |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2306.17847 |