38+15 pages. v3 Corrected the dissipative tail terms, previously taken from Eq. (C12) of Bini et al. [2210.07165], upon recognizing that Eq. (C12) contains additional contributions. The total scattering angle is updated accordingly in the text and ancillary file. All other results are unchanged. The conservative sector is unaltered
Using the worldline action in [2409.05860], we derive the total even-in-velocity (relative) impulse, scattering angle, and time delay at fifth post-Newtonian (5PN) order, including radiation-reaction and hereditary contributions at ${\cal O}(G^5ν^2)$ and ${\cal O}(G^6ν^2)$. We introduce an isotropic-like description which, together with the associated losses of energy and angular momentum, fixes the evolution of the system from scattering data. This framework opens the door to an unambiguous characterization of the underlying two-body dynamics solely in terms of scattering observables. Following [2409.05860], we isolate a conservative component using Feynman's $i0^+$ prescription. This sector contains both "tail-like" and "memory-like" contributions, the latter being nonlocal in time and described by a double Principal-Value integral. Owing to the local-in-time character of the corresponding (in-in) action, we establish a systematic procedure that is consistent with Feynman's prescription while preserving the complete local dynamics. This provides a universal contribution to the conservative (isotropic) Hamiltonian at 5PN order and, as a byproduct, also fixes the value of the Effective One Body coefficients $\{{\bar d}_{5{\rm loc}}, a_{6{\rm loc}}\}$ consistently with the Tutti-Frutti framework. For completeness, we analyse the "$γ\text{-}3$" prescription introduced in recent post-Minkowskian computations. When implemented in our formalism, we find exact agreement over the overlapping regime of validity. In contrast, Feynman's prescription yields a (local) memory-like contribution with the opposite sign at ${\cal O}(G^5ν^2)$. We also find that an analogous $γ\text{-}3$ rerouting at ${\cal O}(G^6ν^2)$ would be incompatible with the conjecture that all $π^2$ terms arise solely from the potential region, while Feynman's formulation preserves this expectation.
Novel approach to binary dynamics: application to the fifth post-Newtonian level
介绍了一种新的方法来推导引力相互作用双星系统的保守动力学。我们的方法以一种新颖的方式结合了几种理论形式：后牛顿，后闵可夫斯基，多极后闵可夫斯基，引力自力和有效的一体。我们应用我们的方法来推导第五后牛顿动力学。通过将我们的结果限制到第三个后Minkowski水平，我们首次独立地证实了Bern { \it et al.} [物理学]修订版本\ Lett. { \bf 122}，201603（2019）]。我们还为未来的第四次后闵可夫斯基计算提供了检查。我们的技术，原则上，可以扩展到更高阶的微扰理论。
Gravitational Compton scattering at the fifth post-Minkowskian order
Scuola Normale Superiore（高等师范学校）；INFN Sezione di Pisa（意大利国家核物理研究所比萨分部）；Dipartimento di Fisica e Astronomia, Università di Padova（帕多瓦大学物理与天文学系）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Higgs Centre for Theoretical Physics, University of Edinburgh（爱丁堡大学希格斯理论物理中心）
Nonlocal-in-time tail effects in gravitational scattering to fifth Post-Minkowskian and tenth self-force orders
II. Institute for Theoretical Physics, Hamburg University（汉堡大学第二理论物理研究所）；Institute for Theoretical Physics, ETH Zürich（苏黎世联邦理工学院理论物理研究所）；School of Physics and Shing-Tung Yau Center, Southeast University（东南大学物理学院暨陈省身数学中心）；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器）
Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. V. Evidence for the strong equivalence principle to second post-Newtonian order
