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Photon sphere and quasinormal modes in AdS/CFT
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Photon spheres are the characteristic of general black holes, thus are a suitable touchstone for the emergence of gravitational spacetime in the AdS/CFT correspondence. We provide a spectral analysis of an AdS Schwarzschild black hole near its photon sphere. We find that quasinormal modes near the photon sphere reflect the AdS boundary, resulting in a peculiar spectral pattern. Our large angular momentum analysis owes to an analogue to solvable Schr\"odinger equations such as an inverted harmonic oscillator and the P\"oschl-Teller model, with a Dirichlet boundary condition. Through the AdS/CFT dictionary, it predicts the existence of a peculiar subsector in the large angular momentum spectrum of thermal holographic CFTs on a sphere.
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Can we distinguish whether black holes have singularities or not through echoes and light rings?
In the Bardeen and Hayward black hole families, the singular type II branch can have two light rings and echo-like quasinormal signals, while regular black holes have one light ring.
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