论文标题
Newtonian在偏心轨道非旋转极端质量比率的旋转式不变性的扩展为9pn和$ e^{16} $
Post-Newtonian expansion of the spin-precession invariant for eccentric-orbit non-spinning extreme-mass-ratio inspirals to 9PN and $e^{16}$
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
We calculate the eccentricity dependence of the high-order post-Newtonian (PN) expansion of the spin-precession invariant $ψ$ for eccentric-orbit extreme-mass-ratio inspirals with a Schwarzschild primary. The series is calculated in first-order black hole perturbation theory through direct analytic expansion of solutions in the Regge-Wheeler-Zerilli formalism, using a code written in \textsc{Mathematica}. Modes with small values of $l$ are found via the Mano-Suzuki-Takasugi (MST) analytic function expansion formalism for solutions to the Regge-Wheeler equation. Large-$l$ solutions are found by applying a PN expansion ansatz to the Regge-Wheeler equation. Previous work has given $ψ$ to 9.5PN order and to order $e^2$ (i.e., the near circular orbit limit). We calculate the expansion to 9PN but to $e^{16}$ in eccentricity. It proves possible to find a few terms that have closed-form expressions, all of which are associated with logarithmic terms in the PN expansion. We also compare the numerical evaluation of our PN expansion to prior numerical calculations of $ψ$ in close orbits to assess its radius of convergence. We find that the series is not as rapidly convergent as the one for the redshift invariant at $r \simeq 10M$ but still yielding $\sim 1\%$ accuracy for eccentricities $e \lesssim 0.25$.
