论文标题
红移不变的高级牛顿后偏移轨道不变的非旋转极端质量比率灵感
High-order post-Newtonian expansion of the redshift invariant for eccentric-orbit non-spinning extreme-mass-ratio inspirals
论文作者
论文摘要
我们计算了高阶纽顿后（PN）系列的偏心依赖性，用于在schwarzschild背景上用于偏心 - 轨道极限质量的extreme-mass-Ratio Inspirals的广义红移$ \ langle u^t \rangle_τ$。这些结果是在使用Regge-Wheeler-Zerilli（RWZ）仪表的一阶黑洞扰动理论（BHPT）中计算的。我们的\ textsc {Mathematica}代码基于一个熟悉的过程，使用Mano-Suzuki-Takasugi（MST）的PN扩展，用于$ l $模式的$ l $模式，然后使用直接的一般$ $ l $ pn扩展，用于任意高$ L $。我们按PN顺序和偏心率计算双重扩展，达到10pn相对顺序和$ e^{20} $。详细了解每个PN顺序的偏心率膨胀，使我们能够在偏心依赖性中找到许多具有已知系数的封闭形式表达式和多个无限序列。我们发现红移不变的PN扩展中的主要对数序列反映了能量通量向无穷大的PN扩展的类似行为。显示出在能量通量中出现的一组通量术语和特殊功能，例如Peters-Mathews Flux本身，在红移PN扩展中会重新出现。
We calculate the eccentricity dependence of the high-order post-Newtonian (PN) series for the generalized redshift invariant $\langle u^t \rangle_τ$ for eccentric-orbit extreme-mass-ratio inspirals on a Schwarzschild background. These results are calculated within first-order black hole perturbation theory (BHPT) using Regge-Wheeler-Zerilli (RWZ) gauge. Our \textsc{Mathematica} code is based on a familiar procedure, using PN expansion of the Mano-Suzuki-Takasugi (MST) analytic function formalism for $l$ modes up to a certain maximum and then using a direct general-$l$ PN expansion of the RWZ equation for arbitrarily high $l$. We calculate dual expansions in PN order and in powers of eccentricity, reaching 10PN relative order and $e^{20}$. Detailed knowledge of the eccentricity expansion at each PN order allows us to find within the eccentricity dependence numerous closed-form expressions and multiple infinite series with known coefficients. We find leading logarithm sequences in the PN expansion of the redshift invariant that reflect a similar behavior in the PN expansion of the energy flux to infinity. A set of flux terms and special functions that appear in the energy flux, like the Peters-Mathews flux itself, are shown to reappear in the redshift PN expansion.
