Extracting information behind the veil of horizon

TL;DR

This paper investigates how boundary correlators in a simplified AdS/CFT model encode information about an artificial singularity inside a black hole, showing that certain parameters can be inferred from these correlators.

Contribution

It explicitly demonstrates that boundary correlators can reflect parameters associated with an artificial singularity within a black hole model, advancing understanding of information encoding in holography.

Findings

Boundary correlators encode information about the artificial singularity.

The parameter of the singularity can be read from correlators in a vacuum state.

The ability to extract information depends on the initial state of the system.

Abstract

In AdS/CFT duality, it is often argued that information behind the event horizon is encoded even in boundary correlators. However, its implication is not fully understood. We study a simple model which can be analyzed explicitly. The model is a two-dimensional scalar field propagating on the s-wave sector of the BTZ black hole formed by the gravitational collapse of a null dust. Inside the event horizon, we placed an artificial timelike singularity where one-parameter family of boundary conditions is permitted. We compute two-point correlators with two operators inserted on the boundary to see if the parameter is reflected in the correlators. In a typical case, we give an explicit form of the boundary correlators of an initial vacuum state and show that the parameter can be read off from them. This does not immediately imply that the asymptotic observer can extract the information of the singularity since one cannot control the initial state in general. Thus, we also study whether the parameter can be read off from the correlators for a class of initial states.