The Black Hole Singularity in AdS/CFT

TL;DR

This paper investigates how the black hole singularity in AdS/CFT is reflected in boundary correlators, revealing signals of the singularity through complex geodesics and their implications for quantum gravity.

Contribution

It demonstrates that the black hole singularity influences boundary correlators via complex geodesics, providing a new method to probe singularities in AdS/CFT.

Findings

Identification of a t_c singularity signaling the black hole singularity

Correlation functions dominated by complexified geodesics

Persistence of the t_c singularity across various theoretical expansions

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. We show that the Penrose diagram for d>3 is not square. As a result, the real geodesic connecting the two boundary points becomes almost null and bounces off the singularity at a finite boundary time t_c \neq 0. 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, whose properties yield the large mass quasinormal mode frequencies previously found for this black hole. We find a 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 of the black hole singularity, occurs on a secondary sheet of the analytically continued correlator. Its properties are computationally accessible. 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.