A signature of the timelike singularity in holography

Abstract

In the context of the AdS/CFT correspondence, we provide a simple observable, the imaginary part of the retarded Green's function, which captures the timelike singularity of a charged black brane. Solving wave equations of bulk fields with different spins outside the black brane, we calculate exponentially small contributions to retarded Green's functions in the dual CFT at large real frequency. These contributions admit an interpretation in terms of paths in an analytically continued classical black brane interior via a WKB approximation: they provide the complex time elapsed along null geodesics that reflect off the singularity, and incorporate the corresponding reflection coefficients.