Spherical orbits around Kerr-Newman and Ghosh black holes

Abstract

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 {\it 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 {\it 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 {\it 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.