发表机构
Universitat de les Illes Balears（巴利阿里群岛大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文用Poincaré-Lindstedt方法求解受扰比内方程，直接确定径向运动频移，从而计算近日点进动，并给出多种扰动下的显式表达式，恢复已知结果并得到新贡献，适用于致密双星及特定度规中的粒子运动。
AI 中文摘要
我们将Poincaré-Lindstedt方法应用于描述受扰开普勒问题保守动力学的受扰比内方程。我们表明，对发散项的简单处理可直接确定径向运动的频移，从而得到近日点进动。我们给出了多项式、对数和逆幂扰动的显式表达式，并将该过程推广到更高阶的微扰以及涉及多个扰动参数的问题。将此方法应用于与致密双星相关的不同物理效应，我们恢复了已知结果。我们还获得了近日点进动的新贡献，包括任意质量型和电流型潮汐多极子以及质量型自旋诱导多极子的领头阶效应，NNLO电流型潮汐四极子贡献，NNLO的电磁电偶极子贡献以及电荷的偏心修正。最后，我们展示了该方法如何直接应用于Reissner-Nordström、de Sitter-Schwarzschild度规和Yukawa势中的粒子运动问题。
英文摘要
We apply the Poincaré-Lindstedt method to the perturbed Binet equation describing conservative dynamics of the perturbed Kepler problem. We show that a simple treatment of divergent terms directly determines the frequency shift of the radial motion and hence the periastron advance. We provide explicit expressions for polynomial, logarithmic and inverse power perturbations, extend the procedure to higher perturbative orders and to problems involving several perturbation parameters. Applying this method to different physical effects relevant to compact binaries, we recover known results. We also obtain new contributions to the periastron advance, including the leading-order effects of arbitrary mass- and current-type tidal multipoles and mass-type spin-induced multipoles, the NNLO current-type tidal quadrupole contribution, electromagnetic electric-dipole contributions to NNLO and the eccentric corrections to the electric charge. Finally, we illustrate how the method can be directly applied to the problem of particle motion in Reissner-Nordström, de Sitter-Schwarzschild metrics and in a Yukawa potential.
Comments13 pages
