AI 中文总结
本文在极端质量比极限下计算出第八后闵可夫斯基阶的引力轫致辐射波形，完善了此前结果，提升了散射波形精度。
AI 中文摘要
在极端质量比极限下，我们于频域计算了两个无自旋天体散射产生的引力波形，其阶次为第八后闵可夫斯基（PM）阶（即$O(G^8)$，对应六圈），同时达到分数第六后牛顿（PN）阶。此前$O(G^4)$阶的结果在此得到完善，我们计算了5PM阶的辐射角动量以及6PM阶的辐射反作用散射角。至该阶次，波形可通过少量主积分表示，其被积函数为（修正）贝塞尔函数的双线性形式，进而得到迭代贝塞尔函数，后者可进一步用梅耶G函数表示。从$O(G^5)$（四圈）阶开始，傅里叶积分的结构变得相当复杂，实际上存在若干新的主积分族，可证明这些主积分满足非齐次贝塞尔方程，且以低阶主积分为源。尽管本结果仅适用于质量比的一阶，但显著提升了散射波形的精度；当前基于量子振幅计算的结果仅达一圈水平，而采用多极后闵可夫斯基形式的结果仅达两圈水平且仅具备2PN精度。
英文摘要
The gravitational waveform generated by the scattering of two nonspinning bodies is computed in the frequency domain in the extreme-mass-ratio limit at the eighth post-Minkowskian (PM) order (i.e., $O(G^8)$, or six-loop) and at the fractional sixth post-Newtonian (PN) order. Previous results at $O(G^4)$ are completed here by computing the 5PM radiated angular momentum as well as the 6PM radiation-reacted scattering angle. Up to that order the waveform is expressed in terms of few master integrals, with integrands bilinear in (modified) Bessel functions, leading to iterated Bessel functions which can be in turn expressed in terms of Meijer G functions. Starting from $O(G^5)$ (four-loop) the structure of Fourier integrals becomes quite involved. In fact, there are several new families of master integrals, which can be shown to satisfy inhomogeneous Bessel equations with master integrals of lower order as sources. Although limited to the first order in the mass ratio, the results presented here significantly improve the accuracy of the scattering waveform, currently known at the one-loop level from quantum-amplitude-based computations or at the two-loop level (but with 2PN accuracy only) by using the multipolar-post-Minkowskian formalism.
Comments10 pages, revtex macros used
