Eccentric orbit binary black hole inspirals: Informing the post-Newtonian expansion through black hole perturbation theory
Eccentric orbit binary black hole inspirals: Informing the post-Newtonian expansion through black hole perturbation theory
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偏心轨道双黑洞螺旋：通过黑洞微扰理论为后牛顿膨胀提供信息
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发表时间：
2018
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通讯作者：
Seth Hopper
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作者：
Christopher Munna;Erik Forseth;C. Evans;Seth Hopper
引力波天文学的时代已经到来。因此，我们现在有机会观察以前人类看不见的宇宙特征。为了推进波探测工作，本论文提出了非旋转双黑洞（BBH）螺旋动力学的新结果。在其中，我重点关注偏心轨道极限质量比螺旋（EMRI），这是一种目前尚未开发的BBH类型，其中轨道具有椭圆形形状，并且两个质量中的一个比另一个质量大得多。我通过结合两种常见的方法（黑洞微扰理论（BHPT）的小质量比近似和后牛顿（PN）理论的小速度近似）来研究这些电磁磁共振成像，以新颖的方式更好地描述它们的演化。 BHPT 使用 Mano-Suzuki-Takasugi 形式主义来研究，将一阶扰动表示为超几何函数的无限和。然后在慢动作状态下分析这些解，以导出可观测量的高阶 PN 级数，特别关注通量：系统辐射的总能量和角动量。使用数值和分析方法分别发现无穷远通量的 BHPT-PN 展开式以比较功效。结果是通过 10PN 导出至少 $e^{20}$ 以及通过 19PN 至少 $e^{10}$ 的通量项。对于中心地平线处的通量，10PN/$e^{20}$ 和 18PN/$e^{10}$ 的结果类似。同时，使用多极后闵可夫斯基 PN 形式主义在 PN 理论中研究无穷远处的通量。通过操纵傅立叶空间中的某些多极矩，我们发现了无限组先前未知的多极贡献。导出主要对数通量项及其 1PN 修正的紧凑形式。对次领先对数及其 1PN 修正进行了大幅简化。为质量比最低阶的完整 4PN 和 6PN 对数通量提取紧凑表达式。最后，应用类似的分析技术来推导两个局部守恒量的新颖 BHPT-PN 展开式：广义红移不变量和自旋进动不变量。前者为 8.5PN 和 $e^{20}$，后者为 6.5PN 和 $e^{16}$。总体而言，本文对 EMRI 的引力辐射和轨道运动有了更深入的理解，并在整体上发现了 BHPT 和 PN 形式主义的新结构。本文包含的结果将有助于分析 LISA 获得的波形数据，LISA 是计划于 2034 年发射的天基引力波探测器。
The era of gravitational-wave astronomy has arrived. As a result, we now have the opportunity to observe features of the universe previously hidden from human view. To advance efforts on wave detection, this dissertation presents new results on the dynamics of non-spinning binary black hole (BBH) inspirals. In it I focus on the eccentric-orbit extreme-mass-ratio inspiral (EMRI), a presently underdeveloped class of BBHs in which the orbit has an elliptical shape and one of the two masses is much larger than the other. I investigate these EMRIs by combining two common approaches --- the small-mass-ratio approximation of black hole perturbation theory (BHPT) and the small-velocity approximation of post-Newtonian (PN) theory --- in novel ways to better describe their evolution. BHPT is studied using the Mano-Suzuki-Takasugi formalism to represent first-order perturbations as infinite summations of hypergeometric functions. These solutions are then analyzed in the slow-motion regime to derive high-order PN series for observable quantities, with particular focus on the fluxes: the total energy and angular momentum radiated by the system. BHPT-PN expansions for the fluxes at infinity are found separately using numerical and analytical approaches to compare efficacy. The result is the derivation of flux terms to at least $e^{20}$ through 10PN and at least $e^{10}$ through 19PN. Results to 10PN/$e^{20}$ and 18PN/$e^{10}$ are similarly found for the fluxes at the central horizon. Simultaneously, the fluxes at infinity are studied within PN theory using the multipolar post-Minkowskian PN formalism. By manipulating certain multipole moments in Fourier space, we find infinite sets of previously unknown multipole contributions. Compact forms are derived for the leading logarithm flux terms and their 1PN corrections. Drastic simplifications are made to the subleading logarithms and their 1PN corrections. Compact expressions are extracted for the full 4PN and 6PN Log fluxes at lowest order in the mass ratio. Finally, similar analytical techniques are applied to derive novel BHPT-PN expansions for two local conserved quantities: the generalized redshift invariant and spin-precession invariant. The former is found to 8.5PN and $e^{20}$ and the latter to 6.5PN and $e^{16}$. Overall, this thesis offers a deeper understanding of the gravitational radiation and orbital motion of EMRIs and finds new structure in the BHPT and PN formalisms as a whole. The results contained herein will contribute to the analysis of waveform data obtained by LISA, the space-based gravitational-wave detector scheduled for launch in 2034.