Classical soft theorems meet the post-Newtonian expansion
Abstract
Classical soft theorems govern the non-analytic structure of electromagnetic and gravitational radiation in the low-frequency regime, with the gravitational memory effect providing the canonical realization of the classical soft graviton theorem. While the soft behavior of radiation from hyperbolic scattering is well understood, its realization in gravitationally bound systems remains less explored. In this work, we study the soft structure of gravitational waveforms generated by compact binaries, focusing on the scattering of emitted radiation off the static background curvature within the multipolar post-Newtonian framework. We isolate the infrared (IR) logarithms associated with hereditary effects, including the tail-of-memory, and their higher generalizations with n-tail insertions. The resulting amplitudes exhibit a Laurent expansion in frequency space consistent with the Sahoo-Sen logarithmic soft theorems, thereby establishing a direct correspondence between gravitational memory effects, their higher-order tail corrections, and the soft expansion. We also comment on ultraviolet (UV) logarithms arising from short-distance sensitivity of the multipole expansion and their associated renormalization-group running.
Related
- All-Orders Classical Soft Graviton Theorems in the Newtonian Limit and Beyond
- Logarithmic corrections to massive particle trajectories for the classical soft log theorems at leading order in G
- Running soft theorems in effective field theory
- All Order Gravitational Wave Tails for Subleading Post-Newtonian Expansion
- Near-horizon soft theorems from local Ward identities
BibTeX
@misc{akhtar2026classical,
title = {{Classical soft theorems meet the post-Newtonian expansion}},
author = {Samim Akhtar and Riccardo Sturani},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.29895},
eprint = {2609.29895},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29895},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Classical soft theorems meet the post-Newtonian expansion
AU - Samim Akhtar
AU - Riccardo Sturani
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2609.29895
UR - https://arxiv.org/abs/2609.29895
AB - Classical soft theorems govern the non-analytic structure of electromagnetic and gravitational radiation in the low-frequency regime, with the gravitational memory effect providing the canonical realization of the classical soft graviton theorem. While the soft behavior of radiation from hyperbolic scattering is well understood, its realization in gravitationally bound systems remains less explored. In this work, we study the soft structure of gravitational waveforms generated by compact binaries, focusing on the scattering of emitted radiation off the static background curvature within the multipolar post-Newtonian framework. We isolate the infrared (IR) logarithms associated with hereditary effects, including the tail-of-memory, and their higher generalizations with n-tail insertions. The resulting amplitudes exhibit a Laurent expansion in frequency space consistent with the Sahoo-Sen logarithmic soft theorems, thereby establishing a direct correspondence between gravitational memory effects, their higher-order tail corrections, and the soft expansion. We also comment on ultraviolet (UV) logarithms arising from short-distance sensitivity of the multipole expansion and their associated renormalization-group running.
ER -