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Circular photon orbit and black hole shadow are significantly importantissues in physics and astronomy, and a number of breakthroughs have beenwitnessed in recent years. Conventionally, the stable and unstable circularphoton orbits are obtained using the effective potential of test particlesmoving in black hole spacetime. In this work, a pure geometric approach isdeveloped to calculate these circular photon orbits and black hole shadowradius. Furthermore, it can be proved that our geometric approach is completelyequivalent to the conventional approach based on effective potentials of testparticles.

Geometric Approach to Circular Photon Orbits and Black Hole Shadows