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Gravitational collapse and its boundary description in AdS

Steven B. Giddings, Aleksey Nudelman

TL;DR

The paper investigates gravitational collapse in AdS and its boundary dual by studying a collapsing dust shell, its classical dynamics, and the quantum scalar field behavior in this background. It shows that a discrete spectrum of boundary excitations arises for a finite shell, which becomes a continuum as the shell approaches the horizon, corresponding to a Boulware-like boundary state, while the physically relevant endpoint is the Hartle-Hawking state with a thermal boundary description. The work clarifies how boundary correlators encode bulk collapse and thermalization, and discusses the challenging transition from a pure shell state to a thermal HH state in the boundary theory, with implications for the black hole information problem. It also connects these ideas to D3-brane shells and suggests directions for understanding information encoding and retrieval in holographic setups.

Abstract

We provide examples of gravitational collapse and black hole formation in AdS, either from collapsing matter shells or in analogy to the Oppenheimer-Sneider solution. We then investigate boundary properties of the corresponding states. In particular, we describe the boundary two-point function corresponding to a shell outside its horizon; if the shell is quasistatically lowered into the horizon, the resulting state is the Boulware state. We also describe the more physical Hartle-Hawking state, and discuss its connection to the quasistatic shell states and to thermalization on the boundary.

Gravitational collapse and its boundary description in AdS

TL;DR

The paper investigates gravitational collapse in AdS and its boundary dual by studying a collapsing dust shell, its classical dynamics, and the quantum scalar field behavior in this background. It shows that a discrete spectrum of boundary excitations arises for a finite shell, which becomes a continuum as the shell approaches the horizon, corresponding to a Boulware-like boundary state, while the physically relevant endpoint is the Hartle-Hawking state with a thermal boundary description. The work clarifies how boundary correlators encode bulk collapse and thermalization, and discusses the challenging transition from a pure shell state to a thermal HH state in the boundary theory, with implications for the black hole information problem. It also connects these ideas to D3-brane shells and suggests directions for understanding information encoding and retrieval in holographic setups.

Abstract

We provide examples of gravitational collapse and black hole formation in AdS, either from collapsing matter shells or in analogy to the Oppenheimer-Sneider solution. We then investigate boundary properties of the corresponding states. In particular, we describe the boundary two-point function corresponding to a shell outside its horizon; if the shell is quasistatically lowered into the horizon, the resulting state is the Boulware state. We also describe the more physical Hartle-Hawking state, and discuss its connection to the quasistatic shell states and to thermalization on the boundary.

Paper Structure

This paper contains 10 sections, 81 equations, 7 figures.

Table of Contents

  1. Introduction
  2. A collapsing shell in AdS
  3. Quantization in the shell background
  4. Classical solutions
  5. Quantization
  6. Boundary description
  7. The Hartle-Hawking Green function and thermalization of the shell state
  8. The Hartle-Hawking state and Green function for Schwarzschild-AdS
  9. Thermalization and approach to the Hartle Hawking state
  10. Discussion

Figures (7)

  • Figure 1: The Penrose diagram for Schwarzschild-AdS.
  • Figure 2: The Penrose diagram for collapsing shell in anti de-Sitter space.
  • Figure 3: The effective potential for $d=4$, $l=0$, $r_H=2$ and $R=5$. The shell lies at $r_*\approx 1.37$ and produces a delta function in the potential, as shown.
  • Figure 4: The effective potential for $d=4$, $l=0$,$r_h=2$ and $R=2.01$. The shell is close to its gravitational radius. Note that the potential in the vicinity of the shell is very small as compared to the case of a large-radius shell, fig. 3. It has also been shifted leftwards; now the shell lies at $r_* \approx 0.7$.
  • Figure 5: Tortoise coordinate $r_*$ position of the shell as a function of $R$. Note that the shell moves to $r_*=-\infty$ as $R\rightarrow r_H=2$.
  • ...and 2 more figures