The Black Hole Singularity in AdS/CFT

We explore physics behind the horizon in eternal AdS Schwarzschild blackholes. In dimension d >3, where the curvature grows large near the singularity,we find distinct but subtle signals of this singularity in the boundary CFTcorrelators. Building on previous work, we study correlation functions ofoperators on the two disjoint asymptotic boundaries of the spacetime byinvestigating the spacelike geodesics that join the boundaries. These dominatethe correlators for large mass bulk fields. We show that the Penrose diagramfor d>3 is not square. As a result, the real geodesic connecting the twoboundary points becomes almost null and bounces off the singularity at a finiteboundary time t_c \neq 0. If this geodesic were to dominate the correlatorthere would be a "light cone" singularity at t_c. However, general propertiesof the boundary theory rule this out. In fact, we argue that the correlator isactually dominated by a complexified geodesic, whose properties yield the largemass quasinormal mode frequencies previously found for this black hole. We finda branch cut in the correlator at small time (in the limit of large mass),arising from coincidence of three geodesics. The t_c singularity, a signal ofthe black hole singularity, occurs on a secondary sheet of the analyticallycontinued correlator. Its properties are computationally accessible. The t_csingularity persists to all orders in the 1/m expansion, for finite \alpha',and to all orders in g_s. Certain leading nonperturbative effects can also bestudied. The behavior of these boundary theory quantities near t_c gives, inprinciple, significant information about stringy and quantum behavior in thevicinity of the black hole singularity.Comment: 49 pages, 6 appendices, 14 figures. v3: typos fixe