A bouncing singularity from a null geodesic sets the convergence of the QNM expansion for the Schwarzschild retarded Green's function.
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AdS exotic compact objects imprint bulk-cone singularities from null geodesics and echoes from trapped waves on CFT Green functions, signaling no horizon.
Derives a cavity thermal product formula relating bouncing geodesic singularities in the retarded Green's function to the quasinormal mode spectrum for Schwarzschild and Schwarzschild-de Sitter black holes inside a reflecting cavity.