AI 中文总结
本文提出有效S-矩阵方法描述黑洞并合低频引力波形，在次领头阶揭示对数项与经典贡献的对应，并识别反冲和记忆修正，建立低频并合信息层次。
AI 中文摘要
我们发展了黑洞并合低频引力波形的在壳描述，超越了领头阶。将强耦合并合视为有效的硬$S$-矩阵数据，我们利用软定理和KMOC形式体系组织其长波响应。在次领头阶，量子软定理包含经典软定理中不存在的对数项。我们证明，这些额外项在完整的KMOC in-in可观测量中，通过单圈辐射振幅与相应的引力子割之间的抵消而消失，恰好留下与引力拖曳和早期加速相关的经典对数贡献。我们还识别了来自残余反冲和Christodoulou非线性记忆的$1/\omega$修正。这些结果揭示了低频下可获取的并合信息层次结构：对数尾部仅依赖于渐近硬数据，反冲探测总辐射动量，而非线性记忆则探测所发射辐射的角分布。
英文摘要
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.
Comments45 pages, 4 figures, 4 tables
