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Black Holes, AdS, and CFTs

Donald Marolf

TL;DR

The paper probes how AdS/CFT shapes the interpretation of black hole entropy and unitarity, proposing that entropy counts the density of boundary-observable states within the vacuum superselection sector. It uses Fefferman-Graham expansions to define the boundary stress tensor and explains the AdS/CFT dictionary linking boundary observables to bulk physics, arguing that unitary evolution is preserved without duplicating information. Cardy-style counting in AdS_3 supports that S_BH matches the count of boundary-generated states, while Bag-of-Gold configurations likely reside in separate sectors or require extended, product theories. The work clarifies when S_BH measures interior states and discusses implications for bulk locality and the structure of quantum gravity in AdS, highlighting open questions about bulk observables beyond the boundary algebra.

Abstract

This brief conference proceeding attempts to explain the implications of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence for black hole entropy in a language accessible to relativists and other non-string theorists. The main conclusion is that the Bekenstein-Hawking entropy S_{BH} is the density of states associated with certain superselections sectors, defined by what may be called the algebra of boundary observables. Interestingly, while there is a valid context in which this result can be restated as "S_{BH} counts all states inside the black hole," there may also be another in which it may be restated as "$S_{BH}$ does not count all states inside the black hole, but only those that are distinguishable from the outside." The arguments and conclusions represent the author's translation of the community's collective wisdom, combined with a few recent results. For the proceedings of the WE-Heraeus-Seminar: Quantum Gravity: Challenges and Perspectives, dedicated to the memory of John A. Wheeler.

Black Holes, AdS, and CFTs

TL;DR

The paper probes how AdS/CFT shapes the interpretation of black hole entropy and unitarity, proposing that entropy counts the density of boundary-observable states within the vacuum superselection sector. It uses Fefferman-Graham expansions to define the boundary stress tensor and explains the AdS/CFT dictionary linking boundary observables to bulk physics, arguing that unitary evolution is preserved without duplicating information. Cardy-style counting in AdS_3 supports that S_BH matches the count of boundary-generated states, while Bag-of-Gold configurations likely reside in separate sectors or require extended, product theories. The work clarifies when S_BH measures interior states and discusses implications for bulk locality and the structure of quantum gravity in AdS, highlighting open questions about bulk observables beyond the boundary algebra.

Abstract

This brief conference proceeding attempts to explain the implications of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence for black hole entropy in a language accessible to relativists and other non-string theorists. The main conclusion is that the Bekenstein-Hawking entropy S_{BH} is the density of states associated with certain superselections sectors, defined by what may be called the algebra of boundary observables. Interestingly, while there is a valid context in which this result can be restated as "S_{BH} counts all states inside the black hole," there may also be another in which it may be restated as " does not count all states inside the black hole, but only those that are distinguishable from the outside." The arguments and conclusions represent the author's translation of the community's collective wisdom, combined with a few recent results. For the proceedings of the WE-Heraeus-Seminar: Quantum Gravity: Challenges and Perspectives, dedicated to the memory of John A. Wheeler.

Paper Structure

This paper contains 5 sections, 4 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Boundary observables and AdS/CFT
  3. Unitiarity and AdS/CFT
  4. The Bekenstein-Hawking Entropy in AdS/CFT
  5. Discussion: Where is the bag of gold?

Figures (2)

  • Figure 1: Moment of time-symmetry in a bag of gold spacetime.
  • Figure 2: Rough conformal diagrams for a) an AdS bag of gold spacetime and b) an asymptotically AdS black hole made by throwing in matter (shaded) through the AdS boundary.