We analyze the singularities of the two-point function in a conformal field theory at finite temperature. In a free theory, the only singularity is along the boundary light cone. In the holographic limit, a new class of singularities emerges since two boundary points can be connected by a nontrivial null geodesic in the bulk, encircling the photon sphere of the black hole. We show that these new singularities are resolved by tidal effects due to the black hole curvature, by solving the string worldsheet theory in the Penrose limit. Singularities in the asymptotically flat black hole geometry are also discussed.
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