Dlapa Christoph, Kälin Gregor, Liu Zhengwen, Porto Rafael A
Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany.
Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark.
Phys Rev Lett. 2024 May 31;132(22):221401. doi: 10.1103/PhysRevLett.132.221401.
Leveraging scattering information to describe binary systems in generic orbits requires identifying local and nonlocal in time tail effects. We report here the derivation of the universal (nonspinning) local in time conservative dynamics at fourth post-Minkowskian order, i.e., O(G^{4}). This is achtieved by computing the nonlocal-in-time contribution to the deflection angle, and removing it from the full conservative value in [C. Dlapa et al., Phys. Rev. Lett. 128, 161104 (2022).PRLTAO0031-900710.1103/PhysRevLett.128.161104; C. Dlapa et al., Phys. Rev. Lett. 130, 101401 (2023).PRLTAO0031-900710.1103/PhysRevLett.130.101401]. Unlike the total result, the integration problem involves two scales-velocity and mass ratio-and features multiple polylogarithms, complete elliptic and iterated elliptic integrals, notably in the mass ratio. We reconstruct the local radial action, center-of-mass momentum and Hamiltonian, as well as the exact logarithmic-dependent part(s), all valid for generic orbits. We incorporate the remaining nonlocal terms for ellipticlike motion to sixth post-Newtonian order. The combined Hamiltonian is in perfect agreement in the overlap with the post-Newtonian state of the art. The results presented here provide the most accurate description of gravitationally bound binaries harnessing scattering data to date, readily applicable to waveform modeling.
利用散射信息来描述处于一般轨道的双星系统需要识别时间上的局部和非局部尾部效应。我们在此报告在第四后闵可夫斯基阶（即(O(G^{4}))）下通用（无自旋）时间局部保守动力学的推导。这是通过计算偏转角的时间非局部贡献，并从[C. Dlapa等人，《物理评论快报》128, 161104 (2022). PRLTAO0031 - 900710.1103/PhysRevLett.128.161104；C. Dlapa等人，《物理评论快报》130, 101401 (2023). PRLTAO0031 - 900710.1103/PhysRevLett.130.101401]中的全保守值中去除它来实现的。与总结果不同，积分问题涉及两个尺度——速度和质量比——并且具有多个多重对数、完全椭圆积分和迭代椭圆积分，特别是在质量比方面。我们重构了局部径向作用、质心动量和哈密顿量，以及精确的对数相关部分，所有这些对于一般轨道都是有效的。我们将类椭圆运动的剩余非局部项纳入到第六后牛顿阶。组合后的哈密顿量在重叠部分与后牛顿领域的现有技术完全一致。这里给出的结果提供了迄今为止利用散射数据对引力束缚双星最精确的描述，可直接应用于波形建模。
