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Black Hole Formation in AdS and Thermalization on the Boundary

Ulf H. Danielsson, Esko Keski-Vakkuri, Martin Kruczenski

TL;DR

The paper studies black hole formation in AdS via a spherically symmetric thin-shell collapse and interprets the process holographically as boundary thermalization. Using Minkowski-space AdS/CFT techniques, it derives boundary two-point functions by matching interior AdS and exterior AdS–BH geometries across the shell, revealing shell-induced resonances (shellons) in the off-equilibrium spectrum. In AdS3, it provides explicit spectra showing that as the shell nears the horizon, poles coalesce toward the real axis and form a cut, with the boundary propagator approaching the thermal propagator in the horizon limit, signaling boundary thermalization. The work discusses timescales and argues that a full dynamical description likely requires a boundary kinetic theory, suggesting a holographic dual for the shell’s equations of motion and linking bulk collapse to boundary transport phenomena.

Abstract

We investigate black hole formation by a spherically collapsing thin shell of matter in AdS space. This process has been suggested to have a holographic interpretation as thermalization of the CFT on the boundary of the AdS space. The AdS/CFT duality relates the shell in the bulk to an off-equilibrium state of the boundary theory which evolves towards a thermal equilibrium when the shell collapses to a black hole. We use 2-point functions to obtain information about the spectrum of excitations in the off-equilibrium state, and discuss how it characterizes the approach towards thermal equilibrium. The full holographic interpretation of the gravitational collapse would require a kinetic theory of the CFT at strong coupling. We speculate that the kinetic equations should be interpreted as a holographic dual of the equation of motion of the collapsing shell.

Black Hole Formation in AdS and Thermalization on the Boundary

TL;DR

The paper studies black hole formation in AdS via a spherically symmetric thin-shell collapse and interprets the process holographically as boundary thermalization. Using Minkowski-space AdS/CFT techniques, it derives boundary two-point functions by matching interior AdS and exterior AdS–BH geometries across the shell, revealing shell-induced resonances (shellons) in the off-equilibrium spectrum. In AdS3, it provides explicit spectra showing that as the shell nears the horizon, poles coalesce toward the real axis and form a cut, with the boundary propagator approaching the thermal propagator in the horizon limit, signaling boundary thermalization. The work discusses timescales and argues that a full dynamical description likely requires a boundary kinetic theory, suggesting a holographic dual for the shell’s equations of motion and linking bulk collapse to boundary transport phenomena.

Abstract

We investigate black hole formation by a spherically collapsing thin shell of matter in AdS space. This process has been suggested to have a holographic interpretation as thermalization of the CFT on the boundary of the AdS space. The AdS/CFT duality relates the shell in the bulk to an off-equilibrium state of the boundary theory which evolves towards a thermal equilibrium when the shell collapses to a black hole. We use 2-point functions to obtain information about the spectrum of excitations in the off-equilibrium state, and discuss how it characterizes the approach towards thermal equilibrium. The full holographic interpretation of the gravitational collapse would require a kinetic theory of the CFT at strong coupling. We speculate that the kinetic equations should be interpreted as a holographic dual of the equation of motion of the collapsing shell.

Paper Structure

This paper contains 4 sections, 51 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Derivation of the correlators
  3. Black hole formation in AdS$_{3}$
  4. Discussion

Figures (2)

  • Figure 1: Potential in the presence of a shell.
  • Figure 2: Flow of the first three poles of H in the complex $\omega$ plane as the shell contracts towards the horizon. In the numerical calculation, we used the parameter values $\nu=1.5$, $r_H=10$ (horizon radius), and the initial radius of the shell is $r_s=10.25$.