论文标题
精确计算黑洞周围旋转的旋转轨道I：一般框架和几乎赤道轨道的结果
Precisely computing bound orbits of spinning bodies around black holes I: General framework and results for nearly equatorial orbits
论文作者
论文摘要
非常大的质量比二进制黑洞系统既是一般相对论的两体问题的清洁限制，又是其作为低频引力波来源的重要性。在最低的顺序下，较小的身体沿着较大黑洞的时空的大地测量运动移动。地点后效应包括重力自我力量，它结合了重力波发射的倒反应以及自旋垂直度的力，这是由于小体旋转与黑洞的空间曲率的耦合所产生的。在本文中，我们描述了一种精确计算黑洞旋转旋转轨道的方法。我们的分析是建立在威特扎尼（Witzany）的开拓性工作中的，该作品演示了如何描述旋转身体对小体旋转中线性顺序的运动。利用这样一个事实，即在大质量比率限制的旋转轨道上，旋转的轨道接近地球学，并且由于范德·梅特（Van de Meent）描述了小体沿黑孔轨道的旋转的进攻，因此使用封闭形式的结果，我们开发了运动的频率域名，可以非常精确地解决。我们检查了一系列具有该公式的轨道，重点是本文，这些轨道是偏心且几乎赤道的轨道（即，轨道的运动是$ \ Mathcal {o}（s）$从赤道平面中淘汰），但小体的旋转是任意方向的。我们在伴侣纸中讨论具有一般小体旋转方向的通用轨道。我们表征了这些轨道的行为，并展示了小体的旋转如何改变影响轨道运动的频率$ω_r$和$ω_DCANT。这些频移变化累积的阶段，这些阶段是直接重力波可观察的，这说明了精确表征这些数量重力波观测的重要性。 （简略）
Very large mass ratio binary black hole systems are of interest both as a clean limit of the two-body problem in general relativity, as well as for their importance as sources of low-frequency gravitational waves. At lowest order, the smaller body moves along a geodesic of the larger black hole's spacetime. Post-geodesic effects include the gravitational self force, which incorporates the backreaction of gravitational-wave emission, and the spin-curvature force, which arises from coupling of the small body's spin to the black hole's spacetime curvature. In this paper, we describe a method for precisely computing bound orbits of spinning bodies about black holes. Our analysis builds off of pioneering work by Witzany which demonstrated how to describe the motion of a spinning body to linear order in the small body's spin. Exploiting the fact that in the large mass-ratio limit spinning-body orbits are close to geodesics and using closed-form results due to van de Meent describing precession of the small body's spin along black hole orbits, we develop a frequency-domain formulation of the motion which can be solved very precisely. We examine a range of orbits with this formulation, focusing in this paper on orbits which are eccentric and nearly equatorial (i.e., the orbit's motion is $\mathcal{O}(S)$ out of the equatorial plane), but for which the small body's spin is arbitrarily oriented. We discuss generic orbits with general small-body spin orientation in a companion paper. We characterize the behavior of these orbits and show how the small body's spin shifts the frequencies $Ω_r$ and $Ω_ϕ$ which affect orbital motion. These frequency shifts change accumulated phases which are direct gravitational-wave observables, illustrating the importance of precisely characterizing these quantities for gravitational-wave observations. (Abridged)
