Black Hole Singularity from OPE

TL;DR

This paper demonstrates how black hole singularities are encoded in boundary CFT correlators through the analytic behavior influenced by bouncing geodesics and stress tensor exchanges, revealing a deep holographic connection.

Contribution

It provides a detailed analysis of how black hole singularities manifest in boundary correlators via the Operator Product Expansion and stress tensor contributions, linking geodesic behavior to CFT singularities.

Findings

Boundary correlator singularities align with bulk bouncing geodesics.

Multi-stress-tensor contributions develop branch point singularities at large conformal dimensions.

Complexified geodesics relate to double-trace operator contributions.

Abstract

Eternal asymptotically AdS black holes are dual to thermofield double states in the boundary CFT. It has long been known that black hole singularities have certain signatures in boundary thermal two-point functions related to null geodesics bouncing off the singularities (bouncing geodesics). In this paper we shed light on the manifestations of black hole singularities in the dual CFT. We decompose the boundary CFT correlator of scalar operators using the Operator Product Expansion (OPE) and focus on the contributions from the identity, the stress tensor, and its products. We show that this part of the correlator develops singularities precisely at the points that are connected by bulk bouncing geodesics. Black hole singularities are thus encoded in the analytic behavior of the boundary correlators determined by multiple stress tensor exchanges. Furthermore, we show that in the limit where the conformal dimension of the operators is large, the sum of multi-stress-tensor contributions develops a branch point singularity as predicted by the geodesic analysis. We also argue that the appearance of complexified geodesics, which play an important role in computing the full correlator, is related to the contributions of the double-trace operators in the boundary CFT.