Effective source for second-order self-force calculations: quasicircular orbits in Schwarzschild spacetime
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| Format: | Preprint |
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2025
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| _version_ | 1866910040680562688 |
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| author | Upton, Samuel D. Wardell, Barry Pound, Adam Warburton, Niels Barack, Leor |
| author_facet | Upton, Samuel D. Wardell, Barry Pound, Adam Warburton, Niels Barack, Leor |
| contents | Recent years have seen the first production of "post-adiabatic" gravitational-waveform models based on second-order gravitational self-force theory. These models rely on calculations of an effective source in the perturbative second-order Einstein equation. Here, for the first time, we detail the calculation of the effective source in a Schwarzschild background, which underlies the second-order self-force results in [Phys. Rev. Lett. 127, 151102 (2021); ibid. 128, 231101 (2022); ibid. 130, 241402 (2023)]. The source is designed for use in the multiscale form of the Lorenz-gauge Einstein equation, decomposed in tensor spherical harmonics, or in the analogous second-order Teukolsky equation. It involves, among other things, contributions from (i) quadratic coupling of first-order field modes, (ii) the slow evolution of first-order fields, (iii) quadratic products of a first-order puncture field, and (iv) the second-order puncture field. We validate each of these pieces through numerical and analytical tests. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_00087 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Effective source for second-order self-force calculations: quasicircular orbits in Schwarzschild spacetime Upton, Samuel D. Wardell, Barry Pound, Adam Warburton, Niels Barack, Leor General Relativity and Quantum Cosmology Recent years have seen the first production of "post-adiabatic" gravitational-waveform models based on second-order gravitational self-force theory. These models rely on calculations of an effective source in the perturbative second-order Einstein equation. Here, for the first time, we detail the calculation of the effective source in a Schwarzschild background, which underlies the second-order self-force results in [Phys. Rev. Lett. 127, 151102 (2021); ibid. 128, 231101 (2022); ibid. 130, 241402 (2023)]. The source is designed for use in the multiscale form of the Lorenz-gauge Einstein equation, decomposed in tensor spherical harmonics, or in the analogous second-order Teukolsky equation. It involves, among other things, contributions from (i) quadratic coupling of first-order field modes, (ii) the slow evolution of first-order fields, (iii) quadratic products of a first-order puncture field, and (iv) the second-order puncture field. We validate each of these pieces through numerical and analytical tests. |
| title | Effective source for second-order self-force calculations: quasicircular orbits in Schwarzschild spacetime |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2508.00087 |