论文标题
分析后的牛顿后能量和角动量扩展，偏心轨道非旋转极端质量比率辐射到无穷大的动量，至19pn
Analytic post-Newtonian expansion of the energy and angular momentum radiated to infinity by eccentric-orbit non-spinning extreme-mass-ratio inspirals to 19PN
论文作者
论文摘要
我们为无穷大的纽顿后（PN）在schwarzschild背景上的偏心轨道极端质量比率灵感（EMRIS）的能量和角动量通量开发了新的高阶结果。该系列是通过在RWZ形式中直接扩展的一阶黑洞扰动理论（BHPT）的直接扩展。通过利用分解和一些计算简化，我们能够将通量计算为19pn，每个pn术语计算为（darwin）偏心率的功率序列为$ e^{10} $。这与先前工作中使用的数字拟合方法有利。我们还将pn项计算为$ e^{20} $至10pn。然后，我们通过对数字数据进行数字数据的几个轨道以及各个220模式的数字数据进行检查，分析了复合能通量扩展的收敛性能，并针对每个轨道进行了各种尝试的重新召集方案。高阶系列和数值计算之间的匹配通常很强，相对误差优于$ 10^{-5} $，除非$ p $（半拉出直肠）很小，而$ e $很大。但是，全流量扩展表现出了卓越的保真度（尤其是在高$ e $的情况下），因为它能够合并PN理论中的其他信息。对于轨道$（p = 10，e = 1/2）$，完整的通量在$ 10^{ - 5} $接近$ 10^{ - 5} $上达到了最佳错误，而220模式的错误表现出比$ 1 \％$的错误。最后，我们描述了一种通过分析谐波坐标中的Schwarzschild Geodesic运动来将这些扩展转换为PN理论的谐波量表的程序。这将促进BHPT与PN理论之间的未来比较。
We develop new high-order results for the post-Newtonian (PN) expansions of the energy and angular momentum fluxes at infinity for eccentric-orbit extreme-mass-ratio inspirals (EMRIs) on a Schwarzschild background. The series are derived through direct expansion of the MST solutions within the RWZ formalism for first-order black hole perturbation theory (BHPT). By utilizing factorization and a few computational simplifications, we are able to compute the fluxes to 19PN, with each PN term calculated as a power series in (Darwin) eccentricity to $e^{10}$. This compares favorably with the numeric fitting approach used in previous work. We also compute PN terms to $e^{20}$ through 10PN. Then, we analyze the convergence properties of the composite energy flux expansion by checking against numeric data for several orbits, both for the full flux and also for the individual 220 mode, with various resummation schemes tried for each. The match between the high-order series and numerical calculations is generally strong, maintaining relative error better than $10^{-5}$ except when $p$ (the semi-latus rectum) is small and $e$ is large. However, the full-flux expansion demonstrates superior fidelity (particularly at high $e$), as it is able to incorporate additional information from PN theory. For the orbit $(p=10, e=1/2)$, the full flux achieves a best error near $10^{-5}$, while the 220 mode exhibits error worse than $1\%$. Finally, we describe a procedure for transforming these expansions to the harmonic gauge of PN theory by analyzing Schwarzschild geodesic motion in harmonic coordinates. This will facilitate future comparisons between BHPT and PN theory.
