论文标题
克尔黑洞周围的球形轨道
Spherical orbits around a Kerr black hole
论文作者
论文摘要
一类已知存在于Kerr黑洞周围的特殊轨道是球形轨道 - 轨道具有恒定的坐标半径，不一定局限于赤道平面。近50年前，威尔金斯首先研究了球形时光轨道。在本文中，我们对这些轨道进行了系统的全面研究，其中包括并扩展了对它们的先前作品。我们首先为这些轨道的参数提供了简化的表单。然后详细分析这些轨道的参数空间；特别是，我们描绘了稳定轨道和不稳定轨道，绑定和未结合的轨道以及前列和逆行轨道之间的边界。最后，我们提供了测量方程的分析解决方案，并说明了这些轨道的一些代表性示例。
A special class of orbits known to exist around a Kerr black hole are spherical orbits -- orbits with constant coordinate radii that are not necessarily confined to the equatorial plane. Spherical time-like orbits were first studied by Wilkins almost 50 years ago. In the present paper, we perform a systematic and thorough study of these orbits, encompassing and extending previous works on them. We first present simplified forms for the parameters of these orbits. The parameter space of these orbits is then analysed in detail; in particular, we delineate the boundaries between stable and unstable orbits, bound and unbound orbits, and prograde and retrograde orbits. Finally, we provide analytic solutions of the geodesic equations, and illustrate a few representative examples of these orbits.
