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.

中文翻译：

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19 阶偏心轨道非自旋极端质量比螺旋辐射到无穷大的能量和角动量的解析后牛顿膨胀

我们为 Schwarzschild 背景上的偏心轨道极端质量比螺旋 (EMRI) 的无穷远能量和角动量通量的后牛顿 (PN) 扩展开发了新的高阶结果。该系列是通过直接扩展一阶黑洞微扰理论 (BHPT) 的 RWZ 形式主义中的 MST 解而导出的。通过利用分解和一些计算简化，我们能够计算到 19PN 的通量，每个 PN 项计算为（达尔文）偏心率的幂级数到 $e^{10}$。这与之前工作中使用的数值拟合方法相比具有优势。我们还计算 PN 项到 $e^{20}$ 到 10PN。然后，我们通过检查几个轨道的数值数据来分析复合能通量扩展的收敛特性，对于全通量和单独的 220 模式，每种模式都尝试了各种恢复方案。高阶级数与数值计算的匹配性一般很强，保持相对误差优于$10^{-5}$，除非$p$（半直肠）小而$e$大。然而，全通量扩展表现出卓越的保真度（特别是在高 $e$ 时），因为它能够结合来自 PN 理论的额外信息。对于轨道$(p=10, e=1/2)$，全通量达到$10^{-5}$附近的最佳误差，而220模式表现出比$1\%$更差的误差。最后，我们通过分析谐波坐标中的 Schwarzschild 测地线运动，描述了将这些扩展转换为 PN 理论的谐波规范的过程。这将有助于未来 BHPT 和 PN 理论之间的比较。