Looking for event horizons using UV-IR relations

A primary goal in holographic theories of gravity is to study the causal structure of spacetime from the field theory point of view. This is a particularly difficult problem when the spacetime has a nontrivial causal structure, such as a black hole. We attempt to study causality through the UV-IR relation between field theory and spacetime quantities, which encodes information about bulk position. We study the UV-IR relations for charged black hole spacetimes in the AdS-CFT correspondence. We find that the UV-IR relations have a number of interesting features, but find little information about the presence of a horizon in the bulk. The scale of Wilson loops is simply related to radial position, whether or not there is a horizon. For time-dependent probes, the part of the history near the horizon only affects the late-time behavior of field theory observables. Static supergravity probes have a finite scale size related to radial position in generic black holes, but there is an interesting logarithmic divergence as the temperature approaches zero.