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Quantitative approaches to information recovery from black holes

Vijay Balasubramanian, Bartlomiej Czech

Abstract

The evaporation of black holes into apparently thermal radiation poses a serious conundrum for theoretical physics: at face value, it appears that in the presence of a black hole quantum evolution is non-unitary and destroys information. This information loss paradox has its seed in the presence of a horizon causally separating the interior and asymptotic regions in a black hole spacetime. A quantitative resolution of the paradox could take several forms: (a) a precise argument that the underlying quantum theory is unitary, and that information loss must be an artifact of approximations in the derivation of black hole evaporation, (b) an explicit construction showing how information can be recovered by the asymptotic observer, (c) a demonstration that the causal disconnection of the black hole interior from infinity is an artifact of the semiclassical approximation. This review summarizes progress on all these fronts.

Quantitative approaches to information recovery from black holes

Abstract

The evaporation of black holes into apparently thermal radiation poses a serious conundrum for theoretical physics: at face value, it appears that in the presence of a black hole quantum evolution is non-unitary and destroys information. This information loss paradox has its seed in the presence of a horizon causally separating the interior and asymptotic regions in a black hole spacetime. A quantitative resolution of the paradox could take several forms: (a) a precise argument that the underlying quantum theory is unitary, and that information loss must be an artifact of approximations in the derivation of black hole evaporation, (b) an explicit construction showing how information can be recovered by the asymptotic observer, (c) a demonstration that the causal disconnection of the black hole interior from infinity is an artifact of the semiclassical approximation. This review summarizes progress on all these fronts.

Paper Structure

This paper contains 44 sections, 70 equations, 2 figures.

Table of Contents

  1. Introduction
  2. General remarks
  3. Virtues and features of a laboratory in AdS space
  4. The scale $\exp{(-S)}$: distinguishing basis microstates
  5. Gravity argument:
  6. CFT argument:
  7. The scale $\exp{(-S)}$: distinguishing superposition microstates
  8. The scale $\exp{(-S)}$: a summary
  9. Black holes as mirrors
  10. Assumption 1
  11. Assumption 2
  12. Assumption 3
  13. Assumption 4
  14. Quantitative approaches
  15. Extremal black holes in $AdS_5\times S^5$
  16. ...and 29 more sections

Figures (2)

  • Figure 1: The Penrose diagram of Schwarzschild-AdS in $d > 3$. In $d=3$, the diagram is a perfect square. Arrows mark the directions of Schwarzschild time $t$ in each region. The dashed line is fixed under the reflection symmetry $t \leftrightarrow -t$.
  • Figure 2: Spacelike geodesics in Schwarzschild-AdS. For initial times $t_0 \in t_c, -t_c$ symmetric geodesics cross the horizon, reverse direction, and escape to the other asymptotic boundary; outside this interval geodesics cannot be symmetric and spacelike. Points in the bulk at $t=0$ are traversed by three distinct spacelike geodesics, precursors of the three sheets of $\mathcal{L}(t_0)$.