We conduct a comprehensive study on spherical orbits around two types of black holes: Kerr–Newman black holes, which are charged, and Ghosh black holes, which are nonsingular. In this work, we consider both null and timelike cases of orbits. Utilizing the Mino formalism, all analytical solutions for the geodesics governing these orbits can be obtained. It turns out that all spherical photon orbits outside the black hole horizons are unstable. In the extremal cases of both models, we obtain the photon boomerangs. The existence of charge in the Kerr–Newman allows the orbits to transition between retrograde and prograde motions, and its increase tends to force the orbits to be more equatorial. On the other hand, the Ghosh black hole, characterized by a regular core and a lack of horizons in certain conditions, presents the possibility of observable stable spherical orbits in the so-called no-horizon condition. As the Ghosh parameter k increases, trajectories tend to exhibit larger latitudinal oscillation amplitudes. We observe that as the Ghosh parameter k increases the trajectories tend to have larger latitudinal oscillation amplitudes. Finally, we investigate the existence of innermost stable spherical orbits (ISSOs). Both black holes demonstrate the appearance of two branches of ISSO radii as a function of the Carter constant \({\mathcal {C}}\). However, there are notable differences in their behavior: in the case of the Kerr–Newman black hole, the branches merge at a critical value, beyond which no ISSO exists, while for the Ghosh black hole, the transcendental nature of the metric function causes the branches to become complex at some finite distance.

我们对两种类型黑洞周围的球形轨道进行了全面的研究：带电的克尔-纽曼黑洞和非奇异的戈什黑洞。在这项工作中，我们考虑了零轨道和类时轨道的情况。利用米诺形式主义，可以获得控制这些轨道的测地线的所有解析解。事实证明，黑洞视界外的所有球形光子轨道都是不稳定的。在两种模型的极端情况下，我们都得到了光子回旋镖。克尔-纽曼中电荷的存在允许轨道在逆行和顺行运动之间转换，并且电荷的增加往往会迫使轨道更加赤道。另一方面，戈什黑洞以规则的核心和在某些条件下缺乏视界为特征，在所谓的无视界条件下呈现出可观测的稳定球形轨道的可能性。随着戈什参数 k 的增加，轨迹往往表现出更大的纬度振荡幅度。我们观察到，随着 Ghosh 参数 k 的增加，轨迹往往具有更大的纬度振荡幅度。最后，我们研究了最内层稳定球形轨道（ISSO）的存在。两个黑洞都展示了 ISSO 半径的两个分支的出现，作为卡特常数 \({\mathcal {C}}\) 的函数。然而，它们的行为存在显着差异：在克尔-纽曼黑洞的情况下，分支在临界值处合并，超过该值则不存在 ISSO，而对于戈什黑洞，度量函数的超越性质导致分支在某个有限距离处变得复杂。