Extracting information behind the veil of horizon

TL;DR

The work addresses whether information about a timelike singularity behind a black hole horizon can be read from boundary correlators in AdS/CFT. It introduces a tractable two-dimensional model of a BTZ-like black hole formed by collapse, with a timelike singularity encoded by a one-parameter boundary condition $c$, and computes bulk and boundary Wightman functions to show that, for a vacuum initial state, the boundary correlator's real part encodes $c$ while the imaginary part remains state-independent. The analysis extends to squeezed initial states, revealing that detectability of the singularity information depends on the initial state and may fail for generic excitations, though certain non-degenerate cases suggest persistence of information. Overall, the paper demonstrates that boundary correlators can carry imprints of behind-the-horizon structure under controlled initial-state assumptions and outlines pathways for applying these ideas to more realistic AdS/CFT setups, including higher dimensions and Euclidean preparations.

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.

Figures (4)

• Figure 1: Penrose diagram of the BTZ black hole formed by the gravitational collapse of a null dust shell. The spacetime for $v<0$ corresponds to $\text{AdS}_3$ with a timelike singularity located at $r=0$. The surface $\Sigma$ is an initial Cauchy surface.
• Figure 2: (color online) The real part of the two-point function $G_0(t_1, 10^{-5}\, ;\, c )$. The dotted, solid, and dashed lines correspond to $c=1$, $c=10$, and $c=100$, respectively.
• Figure 3: Penrose diagram of the time-symmetric spacetime with a collapsing dust shell
• Figure 4: The contour of ${\cal W}$ in the complex $z$ plane. The number $N$ is an arbitrary large positive number with $N\neq 2n+1$.