Action-angle variables of a binary black hole with arbitrary eccentricity, spins, and masses at 1.5 post-Newtonian order
Action-angle variables of a binary black hole with arbitrary eccentricity, spins, and masses at 1.5 post-Newtonian order
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DOI：
10.1103/physrevd.107.103040
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发表时间：
2021-10
影响因子：
5
通讯作者：
Sashwat Tanay;L. Stein;G. Cho
中科院分区：
文献类型：
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作者：
Sashwat Tanay;L. Stein;G. Cho
对双黑洞 (BBH) 动力学进行准确、高效的建模对于通过引力波 (GW) 进行探测至关重要，未来将采用 LIGO/Virgo/KAGRA 和 LISA。对于 GW 社区来说，解决具有任意参数且没有简化（如轨道平均或进动平均）的 BBH 系统的动力学问题是封闭形式的最具挑战性的问题之一。一种可能的方法是使用正则扰动理论，该理论从可积哈密顿系统的未扰动变量构造扰动作用角变量。因此，拥有可积 1.5 后牛顿 (PN) BBH 系统的作用角变量是势在必行的。在本文中，我们继续我们两人在 arXiv:2012.06586 中发起的工作，其中我们提出了 BBH 系统的五分之四的动作，具有任意偏心率、质量和自旋，1.5PN 阶。在这里，我们使用一种通过引入不可测量的相空间坐标来扩展相空间的新方法来计算剩余的第五个动作。我们详细介绍了如何计算所有频率，并概述了如何显式地将动作角度变量转换为通常的位置和动量。这可以解析解决 1.5PN 的动态问题。这为使用正则微扰理论分析求解更高 PN 阶下具有任意质量、自旋和偏心率的 BBH 系统的保守动力学奠定了基础。
Accurate and efficient modeling of the dynamics of binary black holes (BBHs) is crucial to their detection through gravitational waves (GWs), with LIGO/Virgo/KAGRA, and LISA in the future. Solving the dynamics of a BBH system with arbitrary parameters without simplifications (like orbit- or precession-averaging) in closed form is one of the most challenging problems for the GW community. One potential approach is using canonical perturbation theory which constructs perturbed action-angle variables from the unperturbed ones of an integrable Hamiltonian system. Having action-angle variables of the integrable 1.5 post-Newtonian (PN) BBH system is therefore imperative. In this paper, we continue the work initiated by two of us in arXiv:2012.06586, where we presented four out of five actions of a BBH system with arbitrary eccentricity, masses, and spins, at 1.5PN order. Here we compute the remaining fifth action using a novel method of extending the phase space by introducing unmeasurable phase space coordinates. We detail how to compute all the frequencies, and sketch how to explicitly transform from the action-angle variables to the usual positions and momenta. This analytically solves the dynamics at 1.5PN. This lays the groundwork to analytically solve the conservative dynamics of the BBH system with arbitrary masses, spins, and eccentricity, at higher PN order, by using canonical perturbation theory.