Spherically symmetric naked singularity spacetimes are claimed to always have an even number of circular photon orbits, with equal numbers of stable and unstable orbits and zero topological charge.
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Investigation of Circular Photon Orbits in Naked Singularity Spacetimes from a Geometric Method
Spherically symmetric naked singularity spacetimes are claimed to always have an even number of circular photon orbits, with equal numbers of stable and unstable orbits and zero topological charge.