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Black hole unitarity and antipodal entanglement

Gerard 't Hooft

TL;DR

This paper argues for black hole unitarity by enforcing antipodal entanglement between Hawking quanta emitted into opposite hemispheres, mediated by gravitational back-reaction that diagonalizes horizon dynamics into independent partial waves and relates in/out states with a unitary S-matrix. It posits antipodal identification on the horizon, linking region I and II as PT/CPT images, so that the global state is pure while local observations appear thermal, effectively removing the interior region for outside observers. The work additionally proposes a gravitational instanton picture for formation/evaporation, analyzes the odd-ℓ constraint, and discusses broader implications, including black hole hair and how this reshapes our understanding of spacetime topology near horizons.

Abstract

Hawking particles emitted by a black hole are usually found to have thermal spectra, if not exactly, then by a very good approximation. Here, we argue differently. It was discovered that spherical partial waves of in-going and out-going matter can be described by unitary evolution operators independently, which allows for studies of space-time properties that were not possible before. Unitarity dictates space-time, as seen by a distant observer, to be topologically non-trivial. Consequently, Hawking particles are only locally thermal, but globally not: we explain why Hawking particles emerging from one hemisphere of a black hole must be 100 % entangled with the Hawking particles emerging from the other hemisphere. This produces exclusively pure quantum states evolving in a unitary manner, and removes the interior region for the outside observer, while it still completely agrees locally with the laws of general relativity. Unitarity is a starting point; no other assumptions are made. Region I and the diametrically opposite region II of the Penrose diagram represent antipodal points in a PT or CPT relation, as was suggested before. On the horizon itself, antipodal points are identified. A candidate instanton is proposed to describe the formation and evaporation of virtual black holes of the type described here. Some important explanations and discussion points are added. In the latest of the paper, again some minor inaccuracies are corrected.

Black hole unitarity and antipodal entanglement

TL;DR

This paper argues for black hole unitarity by enforcing antipodal entanglement between Hawking quanta emitted into opposite hemispheres, mediated by gravitational back-reaction that diagonalizes horizon dynamics into independent partial waves and relates in/out states with a unitary S-matrix. It posits antipodal identification on the horizon, linking region I and II as PT/CPT images, so that the global state is pure while local observations appear thermal, effectively removing the interior region for outside observers. The work additionally proposes a gravitational instanton picture for formation/evaporation, analyzes the odd-ℓ constraint, and discusses broader implications, including black hole hair and how this reshapes our understanding of spacetime topology near horizons.

Abstract

Hawking particles emitted by a black hole are usually found to have thermal spectra, if not exactly, then by a very good approximation. Here, we argue differently. It was discovered that spherical partial waves of in-going and out-going matter can be described by unitary evolution operators independently, which allows for studies of space-time properties that were not possible before. Unitarity dictates space-time, as seen by a distant observer, to be topologically non-trivial. Consequently, Hawking particles are only locally thermal, but globally not: we explain why Hawking particles emerging from one hemisphere of a black hole must be 100 % entangled with the Hawking particles emerging from the other hemisphere. This produces exclusively pure quantum states evolving in a unitary manner, and removes the interior region for the outside observer, while it still completely agrees locally with the laws of general relativity. Unitarity is a starting point; no other assumptions are made. Region I and the diametrically opposite region II of the Penrose diagram represent antipodal points in a PT or CPT relation, as was suggested before. On the horizon itself, antipodal points are identified. A candidate instanton is proposed to describe the formation and evaporation of virtual black holes of the type described here. Some important explanations and discussion points are added. In the latest of the paper, again some minor inaccuracies are corrected.

Paper Structure

This paper contains 8 sections, 27 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Summary of the calculation of the effective bounce
  3. The domains in the Penrose diagram.
  4. Entangled Hawking particles
  5. A gravitational instanton
  6. On the condition that $\ell$ is odd
  7. Discussion
  8. Conclusion

Figures (1)

  • Figure 1: