High post-Minkowskian gravitational waveform for hyperbolic encounters in the extreme-mass-ratio limit
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915857093885952 |
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| author | Geralico, Andrea |
| author_facet | Geralico, Andrea |
| contents | The frequency-domain waveform emitted by a two-body scattering process is computed in the extreme-mass-ratio limit through the fifth post-Minkowskian (PM) order (i.e., $O(G^5)$) and the fractional sixth post-Newtonian (PN) order. The current accuracy of the scattering waveform obtained by quantum amplitude methods is the one-loop level corresponding to the 3PM order, whereas the 4PM waveform is known up to the 2PN order only as derived within the traditional multipolar-post-Minkowskian formalism. Direct comparison between these waveforms to the first order in the mass ratio shows that they differ at most by the effect of an angular-independent time shift, leading to a complete physical agreement at the same level of accuracy. The new results at the 4PM and 5PM orders thus provide a benchmark for future multiloop calculations. The soft limit of the waveform at the leading order in the small-frequency expansion gives the gravitational wave memory, which is evaluated at the 4PM and 5PM orders. The waveform is also used to obtain the radiated energy at $O(G^6)$, improving its knowledge from 3PN to 6PN level. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_11774 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | High post-Minkowskian gravitational waveform for hyperbolic encounters in the extreme-mass-ratio limit Geralico, Andrea General Relativity and Quantum Cosmology The frequency-domain waveform emitted by a two-body scattering process is computed in the extreme-mass-ratio limit through the fifth post-Minkowskian (PM) order (i.e., $O(G^5)$) and the fractional sixth post-Newtonian (PN) order. The current accuracy of the scattering waveform obtained by quantum amplitude methods is the one-loop level corresponding to the 3PM order, whereas the 4PM waveform is known up to the 2PN order only as derived within the traditional multipolar-post-Minkowskian formalism. Direct comparison between these waveforms to the first order in the mass ratio shows that they differ at most by the effect of an angular-independent time shift, leading to a complete physical agreement at the same level of accuracy. The new results at the 4PM and 5PM orders thus provide a benchmark for future multiloop calculations. The soft limit of the waveform at the leading order in the small-frequency expansion gives the gravitational wave memory, which is evaluated at the 4PM and 5PM orders. The waveform is also used to obtain the radiated energy at $O(G^6)$, improving its knowledge from 3PN to 6PN level. |
| title | High post-Minkowskian gravitational waveform for hyperbolic encounters in the extreme-mass-ratio limit |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2603.11774 |