The Black Hole Singularity in AdS/CFT

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  • 18 June 2003
Abstract
We explore physics behind the horizon in eternal AdS Schwarzschild black holes. In dimension d >3, where the curvature grows large near the singularity, we find distinct but subtle signals of this singularity in the boundary CFT correlators. Building on previous work, we study correlation functions of operators on the two disjoint asymptotic boundaries of the spacetime by investigating the spacelike geodesics that join the boundaries. These dominate the correlators for large mass bulk fields. Surprisingly, the Penrose diagram for d>3 is not square. As a result, we find that at a finite boundary time t_c \neq 0, the real geodesic connecting the two boundary points becomes almost null and bounces off the singularity, passing through a region of high curvature. If this geodesic were to dominate the correlator there would be a "light cone" singularity at t_c. However, general properties of the boundary theory rule this out. In fact, we argue that the correlator is actually dominated by a complexified geodesic (in the limit of large mass), arising from coincidence of three geodesics. The t_c singularity, a signal of the black hole singularity, occurs on a secondary sheet of the analytically continued correlator and is computationally accessible. Our techniques also allow us to calculate the large mass quasinormal mode frequencies previously found for this black hole. The t_c singularity 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 be studied. The behavior of these boundary theory quantities near t_c gives, in principle, significant information about stringy and quantum behavior in the vicinity of the black hole singularity.

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