Quadrupolar bremsstrahlung waveform at the third-and-a-half post-Newtonian accuracy
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
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2026
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| _version_ | 1866918464422150144 |
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| author | Bini, Donato Damour, Thibault Geralico, Andrea |
| author_facet | Bini, Donato Damour, Thibault Geralico, Andrea |
| contents | We study the quadrupolar part of the gravitational waveform $h_{ij}$ (encoded in the helicity-($-2)$ radiative quadrupole moment $U_2 = \frac{1}{2!} \bar m^{i} \bar m^{j } U_{i j} \in\frac{R}{4G} \bar m^{i} \bar m^{j } h_{i j}\equiv W $) emitted during the scattering of two masses. Working within the Multipolar Post-Minkowskian (MPM) formalism, we compute the time-domain value of $U_2$ at the third-and-a-half post-Newtonian (3.5PN) accuracy by using the 3.5PN radiation-reacted quasi-Keplerian representation of the hyperbolic motion. We then explicitly evaluate the {\it frequency-domain} value of $U_2$ up to the 2-loop level, i.e. $ O(G^4)$ contributions to $h_{ij}(ω, θ,ϕ)$, corresponding to $O(G^3)$ contributions to $\hat U_2(ω, θ,ϕ)$. The nonlinear memory contribution to the waveform in the center-of-mass frame is computed too, and checked against the soft-limit of the waveform. The 1-loop truncation of our 3.5PN frequency-domain MPM waveform is found to agree with corresponding existing Effective Field Theory (EFT) results when subtracting the dipolar part of the Veneziano-Vilkovisky supertranslation connecting the MPM and EFT Bondi-Metzner-Sachs (BMS) frames. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21522 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quadrupolar bremsstrahlung waveform at the third-and-a-half post-Newtonian accuracy Bini, Donato Damour, Thibault Geralico, Andrea General Relativity and Quantum Cosmology We study the quadrupolar part of the gravitational waveform $h_{ij}$ (encoded in the helicity-($-2)$ radiative quadrupole moment $U_2 = \frac{1}{2!} \bar m^{i} \bar m^{j } U_{i j} \in\frac{R}{4G} \bar m^{i} \bar m^{j } h_{i j}\equiv W $) emitted during the scattering of two masses. Working within the Multipolar Post-Minkowskian (MPM) formalism, we compute the time-domain value of $U_2$ at the third-and-a-half post-Newtonian (3.5PN) accuracy by using the 3.5PN radiation-reacted quasi-Keplerian representation of the hyperbolic motion. We then explicitly evaluate the {\it frequency-domain} value of $U_2$ up to the 2-loop level, i.e. $ O(G^4)$ contributions to $h_{ij}(ω, θ,ϕ)$, corresponding to $O(G^3)$ contributions to $\hat U_2(ω, θ,ϕ)$. The nonlinear memory contribution to the waveform in the center-of-mass frame is computed too, and checked against the soft-limit of the waveform. The 1-loop truncation of our 3.5PN frequency-domain MPM waveform is found to agree with corresponding existing Effective Field Theory (EFT) results when subtracting the dipolar part of the Veneziano-Vilkovisky supertranslation connecting the MPM and EFT Bondi-Metzner-Sachs (BMS) frames. |
| title | Quadrupolar bremsstrahlung waveform at the third-and-a-half post-Newtonian accuracy |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2604.21522 |