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Spherical orbits around Kerr–Newman and Ghosh black holes

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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 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.

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Acknowledgements

We thank Edward Teo for the discussion on his analytical spherical orbit solutions. We also thank Leonardo B. Putra for the discussion on ISSO. BNJ is supported by the Second Century Fund (C2F), Chulalongkorn University, Thailand. HSR is funded by the Hibah Riset FMIPA UI No. PKS-026/UN2.F3.D/PPM.00.02/2023.

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  1. B. N. Jayawiguna

    Present address: High Energy Physics Theory Group, Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, 10330, Thailand

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  1. Departemen Fisika, FMIPA, Universitas Indonesia, Depok, 16424, Indonesia

    A. S. Alam, L. C. Andaru, B. N. Jayawiguna & H. S. Ramadhan

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Contributions

L.C.A. worked on the solutions and figures for regular black holes. A.S.A. worked on the solutions and figures for Kerr–Newman black holes, as well as hel** revising the manuscript. B.N.J. helped with the Kerr–Newman calculations and editing the manuscript text. H.S.R. conceived the idea for the research topic, helped with the Kerr–Newman and regular black holes calculations, and wrote the main manuscript text. All authors reviewed the manuscript and agreed prior to submission.

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Correspondence to H. S. Ramadhan.

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Alam, A.S., Andaru, L.C., Jayawiguna, B.N. et al. Spherical orbits around Kerr–Newman and Ghosh black holes. Gen Relativ Gravit 56, 79 (2024). https://doi.org/10.1007/s10714-024-03264-2

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