An Effective S-Matrix Approach to Low-Frequency Waveforms from Black Hole Mergers
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/ω 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.
Related
- Accurate waveforms for generic planar-orbit binary black holes: The multipolar effective-one-body model SEOBNRv6EHM
- Search for Eccentric Neutron Star-Black Hole Binaries in Advanced LIGO's Fourth Observing Run using Effective-One-Body Waveforms
- Complex frequency evolution of direct waves from binary black hole mergers
- On the Time-Domain Waveforms Leading to Frequency Comb Spectra
- Dynamical tidal response of neutron stars: From effective field theory to gravitational waveforms
BibTeX
@misc{aoki2026effective,
title = {{An Effective $S$-Matrix Approach to Low-Frequency Waveforms from Black Hole Mergers}},
author = {Katsuki Aoki and Feng-Yin Cheng and Andrea Cristofoli and Yu-tin Huang and Hyun Jeong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10329},
eprint = {2609.10329},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10329},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An Effective S-Matrix Approach to Low-Frequency Waveforms from Black Hole Mergers
AU - Katsuki Aoki
AU - Feng-Yin Cheng
AU - Andrea Cristofoli
AU - Yu-tin Huang
AU - Hyun Jeong
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10329
UR - https://arxiv.org/abs/2609.10329
AB - 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/ω 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.
ER -