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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.09568 |
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Table of Contents:
- This paper systematically revisits the critical orbits of test particles moving in various black hole backgrounds, including the Schwarzschild, Reissner-Nordström, Kerr, and Kerr-Newman spacetimes. We identify the critical orbit cases directly from the root structure of the radial equation, and provide explicit expressions relating the relevant parameters -- energy, angular momentum, and charge-to-mass ratio -- to the critical radius, as well as explicit expressions for the critical orbits in each scenario. Special attention is given to the relationship between the photon spheres, black hole shadows and the critical null geodesics. Extensive numerical results are also provided.