An eikonal-inspired approach to the gravitational scattering waveform
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| Format: | Preprint |
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2023
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| author | Georgoudis, Alessandro Heissenberg, Carlo Russo, Rodolfo |
| author_facet | Georgoudis, Alessandro Heissenberg, Carlo Russo, Rodolfo |
| contents | We revisit the amplitude-based derivation of gravitational waveform for the scattering of two scalar black holes at subleading post-Minkowskian (PM) order. We take an eikonal-inspired approach to the two-massive-particle cut needed in the KMOC framework, as highlighted in arXiv:2308.02125, and show that its effect is to implement a simple change of frame. This clarifies one of the points raised in arXiv:2309.14925 when comparing with the post-Newtonian (PN) results. We then provide an explicit PM expression for the waveform in the soft limit, $ω\to0$, including the first non-universal, $ω\logω$, contribution. Focusing on this regime, we show that the small-velocity limit of our result agrees with the soft limit of the PN waveform of arXiv:2309.14925, provided that the two quantities are written in the same asymptotic frame. Performing the BMS supertranslation that, as discussed in arXiv:2201.11607, is responsible for the $\mathcal O(G)$ static contribution to the asymptotic field employed in the PN literature, we find agreement between the amplitude-based and the PN soft waveform up to and including $G^3/c^5$ order. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_07452 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An eikonal-inspired approach to the gravitational scattering waveform Georgoudis, Alessandro Heissenberg, Carlo Russo, Rodolfo High Energy Physics - Theory General Relativity and Quantum Cosmology We revisit the amplitude-based derivation of gravitational waveform for the scattering of two scalar black holes at subleading post-Minkowskian (PM) order. We take an eikonal-inspired approach to the two-massive-particle cut needed in the KMOC framework, as highlighted in arXiv:2308.02125, and show that its effect is to implement a simple change of frame. This clarifies one of the points raised in arXiv:2309.14925 when comparing with the post-Newtonian (PN) results. We then provide an explicit PM expression for the waveform in the soft limit, $ω\to0$, including the first non-universal, $ω\logω$, contribution. Focusing on this regime, we show that the small-velocity limit of our result agrees with the soft limit of the PN waveform of arXiv:2309.14925, provided that the two quantities are written in the same asymptotic frame. Performing the BMS supertranslation that, as discussed in arXiv:2201.11607, is responsible for the $\mathcal O(G)$ static contribution to the asymptotic field employed in the PN literature, we find agreement between the amplitude-based and the PN soft waveform up to and including $G^3/c^5$ order. |
| title | An eikonal-inspired approach to the gravitational scattering waveform |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2312.07452 |