标题： 高能引力散射和广义相对论二体问题 显示英文标题

标题： High-energy gravitational scattering and the general relativistic two-body problem

摘要： 一种将两个引力相互作用物体的经典散射函数转换为相应的（有效单体）哈密顿描述的技术最近被引入 [Phys. Rev. D {\bf 94}, 104015 (2016)]。 使用这种方法，我们首次在牛顿常数的二阶（即一个经典环）下推导出具有任意（可能相对论性的）相对速度的两个点质量的哈密顿量。 得到的（第二后闵可夫斯基）哈密顿量被发现具有温和的高能结构，我们将其与大质量比双星系统的引力自力研究以及Amati、Ciafaloni和Veneziano的超高能量子散射结果相联系。 我们推导了我们的第二后闵可夫斯基哈密顿量的几个后果：(i) 需要使用特殊的相空间规范以获得温和的高能极限；以及(ii) 关于高角动量、高能圆轨道的（静质量无关）线性Regge轨迹行为的预测。 指出了通过专门数值模拟测试这些预测的方法。 最后，我们指出了将我们的经典结果与两个粒子的量子引力散射振幅联系起来的方法，并敦促振幅专家使用他们的新方法计算标量质量的二环散射振幅，从中可以推导出第三后闵可夫斯基有效单体哈密顿量。 显示英文摘要

摘要： A technique for translating the classical scattering function of two gravitationally interacting bodies into a corresponding (effective one-body) Hamiltonian description has been recently introduced [Phys.\ Rev.\ D {\bf 94}, 104015 (2016)]. Using this technique, we derive, for the first time, to second-order in Newton's constant (i.e. one classical loop) the Hamiltonian of two point masses having an arbitrary (possibly relativistic) relative velocity. The resulting (second post-Minkowskian) Hamiltonian is found to have a tame high-energy structure which we relate both to gravitational self-force studies of large mass-ratio binary systems, and to the ultra high-energy quantum scattering results of Amati, Ciafaloni and Veneziano. We derive several consequences of our second post-Minkowskian Hamiltonian: (i) the need to use special phase-space gauges to get a tame high-energy limit; and (ii) predictions about a (rest-mass independent) linear Regge trajectory behavior of high-angular-momenta, high-energy circular orbits. Ways of testing these predictions by dedicated numerical simulations are indicated. We finally indicate a way to connect our classical results to the quantum gravitational scattering amplitude of two particles, and we urge amplitude experts to use their novel techniques to compute the 2-loop scattering amplitude of scalar masses, from which one could deduce the third post-Minkowskian effective one-body Hamiltonian.