Precisely computing bound orbits of spinning bodies around black holes. I. General framework and results for nearly equatorial orbits
Precisely computing bound orbits of spinning bodies around black holes. I. General framework and results for nearly equatorial orbits
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DOI：
10.1103/physrevd.105.124040
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发表时间：
2022-01
影响因子：
5
通讯作者：
L. Drummond;S. Hughes
中科院分区：
文献类型：
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作者：
L. Drummond;S. Hughes
非常大质量比的双黑洞系统是广义相对论中两体问题的一个干净的限制，以及它们作为低频引力波源的重要性。在最低阶，较小的物体沿着较大黑洞时空的测地线移动。后测地线效应包括引力自作用力，它包含了引力波发射的反作用，以及自旋曲率力，它来自于小天体的自旋与黑洞时空曲率的耦合。本文描述了一种精确计算自旋体绕黑洞的束缚轨道的方法。我们的分析建立在Witzany的开创性工作的基础上，该工作演示了如何描述旋转体在小天体旋转中的线性顺序运动。利用大质量比极限自旋体轨道接近测地线这一事实，并利用货车de Meent描述小天体自旋沿着黑洞轨道进动的封闭形式结果，我们发展了一个可以精确求解的运动频域公式.我们研究了一系列的轨道与此公式，重点在本文的轨道是偏心和近赤道（即，轨道的运动是$\mathcal{O}（S）$出赤道平面），但小天体的自旋是任意定向的。我们讨论一般轨道一般小体自旋取向的配套文件。我们描述了这些轨道的行为，并显示了小天体的自旋如何改变影响轨道运动的频率$\Omega_r$和$\Omega_\phi$。这些频移改变了作为直接引力波观测量的累积相位，说明了精确表征这些量对引力波观测的重要性。（节录）
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 $\Omega_r$ and $\Omega_\phi$ 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)