According to general relativity, astrophysical black holes are described by a small number of parameters. Apart from the mass of the black hole (M), among the most interesting characteristics is the spin (a), which determines the degree of rotation, i.e., the angular momentum of the black hole. The latter is observationally constrained by the spectral and timing properties of the radiation signal emerging from an accretion disk of matter orbiting near the event horizon. In the case of the planar (standard, equatorial) accretion disk, this is the location of the innermost stable circular orbit that determines the observable radiation characteristics and allows us to measure the spin. In this paper, we discuss a more general case of the innermost stable spherical orbits (ISSOs) extending above and below the equatorial plane. To this end, we study the nonequatorial geodesic motion of particles following inclined, spherical, relativistically precessing trajectories with the aim of exploring the boundary between the regions of stable (energetically bound) and escaping (energetically unbound) motion. The concept of the radius of the ISSO should play a role in determining the inner rim of a tilted or geometrically thick accretion flow. We demonstrate that the region of inclined bound orbits has a complicated structure due to enhanced precession near the inner rim. We also explore the fate of particles launched below the radius of the marginally bound spherical orbit: these may either plunge into the event horizon or escape to radial infinity.

中文翻译：

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关于旋转黑洞附近最内稳定的球形轨道：暴跌区域附近粒子运动的数值研究

根据广义相对论，天体物理黑洞是由少量参数描述的。除了黑洞的质量（中号），最有趣的特征之一是自旋（A），它决定了旋转的程度，即黑洞的角动量。后者在观测上受到从事件视界附近绕轨道运行的物质吸积盘发出的辐射信号的光谱和定时特性的限制。在平面（标准、赤道）吸积盘的情况下，这是最里面稳定圆形轨道的位置，它决定了可观测的辐射特性并允许我们测量自旋。在本文中，我们讨论了在赤道平面上方和下方延伸的最内稳定球形轨道（ISSO）的更一般情况。为此，我们研究粒子遵循倾斜、球形、相对论进动轨迹的非赤道测地运动，目的是探索稳定（能量束缚）和逃逸（能量无束缚）运动区域之间的边界。 ISSO 半径的概念应该在确定倾斜或几何厚度吸积流的内缘时发挥作用。我们证明，由于内缘附近进动增强，倾斜束缚轨道区域具有复杂的结构。我们还探索了在边缘约束球形轨道半径以下发射的粒子的命运：这些粒子可能会陷入事件视界或逃逸到径向无穷大。