  Lorentzian correlators of local operators exhibit surprising singularities in
theories with gravity duals. These are associated with null geodesics in an
emergent bulk geometry. We analyze singularities of the thermal response
function dual to propagation of waves on the AdS Schwarzschild black hole
background. We derive the analytic form of the leading singularity dual to a
bulk geodesic that winds around the black hole. Remarkably, it exhibits a
boundary group velocity larger than the speed of light, whose dual is the
angular velocity of null geodesics at the photon sphere. The strength of this
singularity is controlled by the classical Lyapunov exponent associated with
the instability of nearly bound photon orbits. In this sense, the bulk-cone
singularity can be identified as the universal feature that encodes the
ubiquitous black hole photon sphere in a dual holographic CFT. To perform the
computation analytically, we express the two-point correlator as an infinite
sum over Regge poles, and then evaluate this sum using WKB methods. We also
compute the smeared correlator numerically, which in particular allows us to
check and support our analytic predictions. We comment on the resolution of
black hole bulk-cone singularities by stringy and gravitational effects into
black hole bulk-cone "bumps". We conclude that these bumps are robust, and
could serve as a target for simulations of black hole-like geometries in
table-top experiments.
