黑洞对II的动力学：球形轨道和变倍旋度的同宿极限
Dynamics of Black Hole Pairs II: Spherical Orbits and the Homoclinic Limit of Zoom-Whirliness
摘要：
自旋黑洞对表现出一系列复杂的动力学行为。具有讽刺意味的是，对偏心和变焦旋转轨道的兴趣激发了本文的重点：恒定半径轨道。当黑洞的自旋不对齐时，恒定半径的轨道就不是圆，而是位于球面上，因此被称为“球面轨道”。球形轨道是重要的，因为它们在能量上框定了所有轨道的分布。此外，每个不稳定的球形轨道都渐近地接近一个旋转无限次的轨道，称为同宿轨道。同宿轨线是一个无限的回旋极限的变焦旋转频谱，并有进一步的意义，作为分界线之间的螺旋和暴跌偏心轨道。我们工作的背景下，两个自旋黑洞的质量相当的3PN哈密顿与自旋轨道耦合。因此，结果可以提供PN展开的准确性的测试基础。此外，球形轨道可以为数值相对论提供有用的初始数据。最后，我们指出，自旋黑洞对应该让位于混沌周围的同宿轨道时，自旋自旋耦合。
英文摘要：
Spinning black hole pairs exhibit a range of complicated dynamical behaviors. An interest in eccentric and zoom-whirl orbits has ironically inspired the focus of this paper: the constant radius orbits. When black hole spins are misaligned, the constant radius orbits are not circles but rather lie on the surface of a sphere and have acquired the name "spherical orbits". The spherical orbits are significant as they energetically frame the distribution of all orbits. In addition, each unstable spherical orbit is asymptotically approached by an orbit that whirls an infinite number of times, known as a homoclinic orbit. A homoclinic trajectory is an infinite whirl limit of the zoom-whirl spectrum and has a further significance as the separatrix between inspiral and plunge for eccentric orbits. We work in the context of two spinning black holes of comparable mass as described in the 3PN Hamiltonian with spin-orbit coupling included. As such, the results could provide a testing ground of the accuracy of the PN expansion. Further, the spherical orbits could provide useful initial data for numerical relativity. Finally, we comment that the spinning black hole pairs should give way to chaos around the homoclinic orbit when spin-spin coupling is incorporated.
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