Excursions beyond the horizon: Black hole singularities in Yang-Mills theories (I)

TL;DR

This paper explores how black hole singularities are represented in the dual conformal field theory via correlation functions, establishing a link between bulk geodesics and boundary observables to probe regions near the singularity.

Contribution

It introduces a direct relation between bulk space-like geodesics and boundary correlators, enabling the study of black hole singularities through CFT data.

Findings

Correlation functions exhibit exponential falloff at large imaginary frequencies.

New gauge-invariant observables reflect the presence of singularities.

A UV/UV connection links physics inside the horizon to boundary data.

Abstract

We study black hole singularities in the AdS/CFT correspondence. These singularities show up in CFT in the behavior of finite-temperature correlation functions. We first establish a direct relation between space-like geodesics in the bulk and momentum space Wightman functions of CFT operators of large dimensions. This allows us to probe the regions inside the horizon and near the singularity using the CFT. Information about the black hole singularity is encoded in the exponential falloff of finite-temperature correlators at large imaginary frequency. We construct new gauge invariant observables whose divergences reflect the presence of the singularity. We also find a UV/UV connection that governs physics inside the horizon. Additionally, we comment on the possible resolution of the singularity.