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arXiv · 2609.10329

An Effective $S$-Matrix Approach to Low-Frequency Waveforms from Black Hole Mergers

Katsuki Aoki·Feng-Yin Cheng·Andrea Cristofoli·Yu-tin Huang·Hyun Jeong
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Abstract

We develop an on-shell description of low-frequency gravitational waveforms from black-hole mergers beyond leading order. Treating the strongly coupled merger as effective hard $S$-matrix data, we organize its long-wavelength response using soft theorems and the KMOC formalism. At next-to-leading order, the quantum soft theorem contains logarithmic terms absent from the classical soft theorem. We show that these extra terms cancel in the full KMOC in-in observable between the one-loop radiative amplitude and the corresponding graviton cut, leaving precisely the classical logarithmic contributions associated with gravitational drag and early-time acceleration. We also identify the $1/\omega$ corrections from remnant recoil and Christodoulou non-linear memory. These results reveal a hierarchy of merger information accessible at low frequency: logarithmic tails depend only on asymptotic hard data, recoil probes total radiated momentum, while non-linear memory probes the angular distribution of the emitted radiation.

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Katsuki Aoki, Feng-Yin Cheng, Andrea Cristofoli, Yu-tin Huang, Hyun Jeong. 2026-09-09. An Effective $S$-Matrix Approach to Low-Frequency Waveforms from Black Hole Mergers. https://arxiv.org/abs/2609.10329

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