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An Infalling Observer in AdS/CFT

Kyriakos Papadodimas, Suvrat Raju

TL;DR

The paper develops a boundary/CFT framework to describe local bulk physics for an observer falling into a big AdS black hole. By reconstructing bulk operators from generalized free fields and employing a thermofield-doubled structure, the authors extend the reconstruction behind the horizon using tilde operators, arguing that interior spacetime is encoded in the single CFT and is smooth at leading order in 1/N. They show that information is preserved through small, nonperturbative corrections and that, at low energies and large N, infalling observers do not encounter firewalls or fuzzball-like structures, while the full microstate of the black hole would require exponentially suppressed measurements to resolve. This framework provides a concrete realization of black hole complementarity within AdS/CFT and offers a detailed counterpoint to firewall and fuzzball proposals, with implications for the information paradox and the role of horizon microstates.

Abstract

We describe the experience of an observer falling into a black hole using the AdS/CFT correspondence. In order to do this, we reconstruct the local bulk operators measured by the observer along his trajectory outside the black hole. We then extend our construction beyond the black hole horizon. We show that this is possible because of an effective doubling of the observables in the boundary theory, when it is in a pure state that is close to the thermal state. Our construction allows us to rephrase questions about information-loss and the structure of the metric at the horizon in terms of more familiar CFT correlators. It suggests that to precisely identify black-hole microstates, the observer would need to conduct measurements to an accuracy of e^{-S_{BH}}. This appears to be inconsistent with the fuzzball proposal, and other recent proposals in which pure states in the ensemble of the black hole are represented by macroscopically distinct geometries. Furthermore, our description of the black hole interior in terms of CFT operators provides a natural realization of black hole complementarity and a method of preserving unitarity without firewalls.

An Infalling Observer in AdS/CFT

TL;DR

The paper develops a boundary/CFT framework to describe local bulk physics for an observer falling into a big AdS black hole. By reconstructing bulk operators from generalized free fields and employing a thermofield-doubled structure, the authors extend the reconstruction behind the horizon using tilde operators, arguing that interior spacetime is encoded in the single CFT and is smooth at leading order in 1/N. They show that information is preserved through small, nonperturbative corrections and that, at low energies and large N, infalling observers do not encounter firewalls or fuzzball-like structures, while the full microstate of the black hole would require exponentially suppressed measurements to resolve. This framework provides a concrete realization of black hole complementarity within AdS/CFT and offers a detailed counterpoint to firewall and fuzzball proposals, with implications for the information paradox and the role of horizon microstates.

Abstract

We describe the experience of an observer falling into a black hole using the AdS/CFT correspondence. In order to do this, we reconstruct the local bulk operators measured by the observer along his trajectory outside the black hole. We then extend our construction beyond the black hole horizon. We show that this is possible because of an effective doubling of the observables in the boundary theory, when it is in a pure state that is close to the thermal state. Our construction allows us to rephrase questions about information-loss and the structure of the metric at the horizon in terms of more familiar CFT correlators. It suggests that to precisely identify black-hole microstates, the observer would need to conduct measurements to an accuracy of e^{-S_{BH}}. This appears to be inconsistent with the fuzzball proposal, and other recent proposals in which pure states in the ensemble of the black hole are represented by macroscopically distinct geometries. Furthermore, our description of the black hole interior in terms of CFT operators provides a natural realization of black hole complementarity and a method of preserving unitarity without firewalls.

Paper Structure

This paper contains 59 sections, 245 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Reconstructing local bulk observables in empty AdS
  3. Properties of generalized free field modes about the vacuum
  4. An Analysis of the Wightman 2-Point Function
  5. Fourier Transform
  6. Local operators on the Poincare patch
  7. Local operators behind the Poincare horizon
  8. Continuing the CFT from ${\mathbb R}^{d-1,1}$ to ${\mathbb S}^{d-1} \times {\mathbb R}$
  9. Discussion
  10. Black holes in AdS: setup and review
  11. Collapsing stars and eternal black holes
  12. Classical Properties of the AdS eternal black hole
  13. How we take the Large $N$ Limit
  14. Quantization in an eternal AdS black hole
  15. Reconstructing the black hole from the boundary, outside the horizon
  16. ...and 44 more sections

Figures (7)

  • Figure 1: Wightman Function
  • Figure 2: Local operators in global AdS using the boundary of the Poincare patch
  • Figure 3: Collapse vs eternal black hole in AdS
  • Figure 4: Kruskal diagram of AdS eternal black hole. As the observer (L) dives in later, it gets increasingly difficult for any signal from an earlier observer (E) to reach him.
  • Figure 5: Cauchy slice for the eternal AdS black brane geometry.
  • ...and 2 more figures