Comparing One-loop Gravitational Bremsstrahlung Amplitudes to the Multipolar-Post-Minkowskian Waveform
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913222713409536 |
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| author | Bini, Donato Damour, Thibault Geralico, Andrea |
| author_facet | Bini, Donato Damour, Thibault Geralico, Andrea |
| contents | We compare recent one-loop-level, scattering-amplitude-based, computations of the classical part of the gravitational bremsstrahlung waveform to the frequency-domain version of the corresponding
Multipolar-Post-Minkowskian waveform result. When referring the one-loop result to the classical averaged momenta $\bar p_a = \frac12 (p_a+p'_a)$, the two waveforms are found to agree at the Newtonian and first post-Newtonian levels, as well as at the first-and-a-half post-Newtonian level, i.e. for the leading-order quadrupolar tail. However, we find that there are significant differences at the second-and-a-half post-Newtonian level, $O\left( \frac{G^2}{c^5} \right)$, i.e. when reaching: (i) the first post-Newtonian correction to the linear quadrupole tail; (ii) Newtonian-level linear tails of higher multipolarity (odd octupole and even hexadecapole); (iii) radiation-reaction effects on the worldlines; and (iv) various contributions of cubically nonlinear origin (notably linked to the quadrupole$\times$ quadrupole$\times$ quadrupole coupling in the wavezone). These differences are reflected at the sub-sub-sub-leading level in the soft expansion, $ \sim ω\ln ω$, i.e. $O\left(\frac{1}{t^2} \right)$ in the time domain. Finally, we computed the first four terms of the low-frequency expansion of the Multipolar-Post-Minkowskian waveform and checked that they agree with the corresponding existing classical soft graviton results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_14925 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Comparing One-loop Gravitational Bremsstrahlung Amplitudes to the Multipolar-Post-Minkowskian Waveform Bini, Donato Damour, Thibault Geralico, Andrea General Relativity and Quantum Cosmology We compare recent one-loop-level, scattering-amplitude-based, computations of the classical part of the gravitational bremsstrahlung waveform to the frequency-domain version of the corresponding Multipolar-Post-Minkowskian waveform result. When referring the one-loop result to the classical averaged momenta $\bar p_a = \frac12 (p_a+p'_a)$, the two waveforms are found to agree at the Newtonian and first post-Newtonian levels, as well as at the first-and-a-half post-Newtonian level, i.e. for the leading-order quadrupolar tail. However, we find that there are significant differences at the second-and-a-half post-Newtonian level, $O\left( \frac{G^2}{c^5} \right)$, i.e. when reaching: (i) the first post-Newtonian correction to the linear quadrupole tail; (ii) Newtonian-level linear tails of higher multipolarity (odd octupole and even hexadecapole); (iii) radiation-reaction effects on the worldlines; and (iv) various contributions of cubically nonlinear origin (notably linked to the quadrupole$\times$ quadrupole$\times$ quadrupole coupling in the wavezone). These differences are reflected at the sub-sub-sub-leading level in the soft expansion, $ \sim ω\ln ω$, i.e. $O\left(\frac{1}{t^2} \right)$ in the time domain. Finally, we computed the first four terms of the low-frequency expansion of the Multipolar-Post-Minkowskian waveform and checked that they agree with the corresponding existing classical soft graviton results. |
| title | Comparing One-loop Gravitational Bremsstrahlung Amplitudes to the Multipolar-Post-Minkowskian Waveform |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2309.14925 |