自旋黑洞的同宿轨道I：Kerr分界线的精确解
Homoclinic Orbits around Spinning Black Holes I: Exact Solution for the Kerr Separatrix
摘要：
在引力辐射的耗散作用下，黑洞双星将从螺旋转变为暴跌。结合轨道和俯冲轨道之间的分界线在过渡中具有显著的特征。对于赤道克尔轨道，我们表明，分界线是一个同宿轨道在一对一的对应关系，一个能量绑定，不稳定的圆形轨道。在提供了同宿轨道的定义，我们利用它们的对应关系与圆形轨道，并推导出精确的解决方案。本文重点讨论物理空间中的同宿行为，而在配套文件中，我们画的互补相空间的肖像。克尔分界线的精确结果可能是有用的解析或数值研究的过渡从螺旋陷入。
英文摘要：
Under the dissipative effects of gravitational radiation, black hole binaries will transition from an inspiral to a plunge. The separatrix between bound and plunging orbits features prominently in the transition. For equatorial Kerr orbits, we show that the separatrix is a homoclinic orbit in one-to-one correspondence with an energetically-bound, unstable circular orbit. After providing a definition of homoclinic orbits, we exploit their correspondence with circular orbits and derive exact solutions for them. This paper focuses on homoclinic behavior in physical space, while in a companion paper we paint the complementary phase space portrait. The exact results for the Kerr separatrix could be useful for analytic or numerical studies of the transition from inspiral to plunge.
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