尾对尾相互作用诱导的高后牛顿阶动力学：非测地项
High-Post-Newtonian-Order Dynamics Induced by Tail-of-Tail Interactions: The Non-Geodesic Terms
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中文总结 AI 辅助
该研究计算偏心无自旋致密双星的尾对尾相互作用贡献，推导高后牛顿阶平均哈密顿量并匹配EOB描述，得到非测地势贡献，重现一阶自引力结果并给出二阶新预测，还推导了相关红移项。
中文摘要 AI 辅助
我们计算偏心、无自旋致密双星保守动力学的尾对尾贡献，达到相对1PN阶和$\mathcal O(e_t^{12})$阶。采用谐坐标系下的1PN准开普勒动力学，我们推导了5.5PN和6.5PN阶的德洛内平均哈密顿量，并将其与有效一体（EOB）描述匹配，从而确定非测地EOB Q势中对应到$\mathcal O(p_r^{12})$阶的贡献，包括对对称质量比的依赖到$\mathcal O(\nu^2)$阶。质量比线性项重现了现有一阶自引力结果，而二次项提供了由尾对尾项产生的定性新的偏心二阶自引力预测。我们通过遗传相互作用的傅里叶-贝塞尔分解独立重新推导了平均哈密顿量。应用固定轨道频率下的第一定律，我们通过$\mathcal O(e^{12})$阶重现了已知的一阶自引力红移，并在5.5PN和6.5PN阶通过$\mathcal O(e^{10})$阶获得了二阶逆红移中完整的尾对尾贡献。
英文摘要
We compute the tail-of-tail contribution to the conservative dynamics of eccentric, non-spinning compact binaries to relative 1PN order and to $\mathcal O(e_t^{12})$. Using the $1$PN quasi-Keplerian dynamics in harmonic coordinates, we derive the Delaunay-averaged Hamiltonian at $5.5$PN and $6.5$PN order and match it to the effective-one-body description, allowing us to determine the corresponding contributions to the non-geodesic EOB $Q$ potential through the $\mathcal{O}(p_r^{12})$, including the dependence on the symmetric mass ratio up to $\mathcal{O}(ν^2)$. The terms linear in the mass ratio reproduce the available first-order self-force results, while the quadratic terms provide qualitatively new eccentric second-order self-force predictions arising from the tail-of-tail terms. We independently rederive the averaged Hamiltonian using a Fourier--Bessel decomposition of the hereditary interaction. Applying the first law at fixed orbital frequencies, we recover the known first-order self-force redshift through $\mathcal O(e^{12})$ and obtain the complete tail-of-tail contribution to the second-order inverse redshift at $5.5$PN and $6.5$PN through $\mathcal O(e^{10})$.
