Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Black Holes as Rubik's Cubes

Bartłomiej Czech, Klaus Larjo, Moshe Rozali

TL;DR

The paper tackles the black hole information paradox by proposing a unitary toy framework in which the interior–exterior entanglement turns around as the black hole evaporates. It introduces information-free horizons and niceness conditions, and demonstrates that entanglement need not grow without bound if the evaporation process terminates in a vacuum state and a mass-dependent, information-free Hawking output is maintained. Through a progression of models culminating in a Final Model, it shows how negative-energy Hawking quanta can drive interior evolution toward a vacuum while preserving unitarity and allowing external observers to glean information via the evaporation timeline. The information retrieval analysis, including a parity-qubit example and Cayley-graph methods, suggests a calculable, finite timescale for reconstructing initial interior data, offering a novel quantum-cosmological route for information escape and pointing to the limits of semiclassical intuition at late stages of evaporation.

Abstract

We propose a unitary toy model of black hole evaporation, in which the entanglement between the interior and exterior degrees of freedom vanishes at late times. Our model possesses the information-free property and satisfies the niceness conditions discussed in the literature. A key feature of the model is that the Hilbert space of black hole internal states contains a vacuum state corresponding to the completely evaporated black hole, which can be reached from any initial state via the Hawking process. Our model suggests a novel quantum cosmological way in which information can get out of an evaporating black hole.

Black Holes as Rubik's Cubes

TL;DR

The paper tackles the black hole information paradox by proposing a unitary toy framework in which the interior–exterior entanglement turns around as the black hole evaporates. It introduces information-free horizons and niceness conditions, and demonstrates that entanglement need not grow without bound if the evaporation process terminates in a vacuum state and a mass-dependent, information-free Hawking output is maintained. Through a progression of models culminating in a Final Model, it shows how negative-energy Hawking quanta can drive interior evolution toward a vacuum while preserving unitarity and allowing external observers to glean information via the evaporation timeline. The information retrieval analysis, including a parity-qubit example and Cayley-graph methods, suggests a calculable, finite timescale for reconstructing initial interior data, offering a novel quantum-cosmological route for information escape and pointing to the limits of semiclassical intuition at late stages of evaporation.

Abstract

We propose a unitary toy model of black hole evaporation, in which the entanglement between the interior and exterior degrees of freedom vanishes at late times. Our model possesses the information-free property and satisfies the niceness conditions discussed in the literature. A key feature of the model is that the Hilbert space of black hole internal states contains a vacuum state corresponding to the completely evaporated black hole, which can be reached from any initial state via the Hawking process. Our model suggests a novel quantum cosmological way in which information can get out of an evaporating black hole.

Paper Structure

This paper contains 16 sections, 20 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Information-free horizons, niceness conditions and the growth of entanglement entropy
  3. A note on small corrections:
  4. The models
  5. The strategy
  6. An example -- the Rubik's cube:
  7. Trial models
  8. Model I -- Full randomness
  9. Strengths and weaknesses:
  10. Model II -- The hidden hand
  11. Strengths and weaknesses:
  12. Model III -- The depository
  13. The Final Model
  14. Properties and interpretation:
  15. Information retrieval
  16. ...and 1 more sections

Figures (3)

  • Figure 1: Entanglement entropies as functions of time for Models I (left) and II (right). In both cases the entropy reaches a maximum and turns around after some time step. The turn-around time and other details of the plots depend on the model and the initial state.
  • Figure 2: Entanglement entropy versus time in the Final Model. For computational reasons, this plot was obtained in a simplified version of the model, in which Rubik's cubes or square tableaux were replaced with copies of a simpler puzzle with only six discrete configurations.
  • Figure 3: $p^{\rm B}_{m,\rm even}$ of state (\ref{['exinitial']}) starts out equal to $p^{{\rm B},\otimes}_{m,{\rm even}}$, but approaches $p^{\rm C}_{\rm even}=2/3$.