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On the partner particles for moving mirror radiation and black hole evaporation

M. Hotta, R. Schützhold, W. G. Unruh

TL;DR

This paper defines and constructs partner modes associated with Hawking-like radiation in black-hole and moving-mmirror setups. By enforcing purity of the Hawking+partner sector and a second condition that ties Hawking and partner creation/annihilation events, the authors show that partner modes can be nonlocal and even reside in regions locally indistinguishable from vacuum. They extend the construction to detectors and amplifiers, deriving explicit expressions for partner wavefunctions and showing that partners often carry no local energy despite carrying correlations with emitted quanta, with long tails and horizon-crossing behavior. The results challenge the notion that information released by black holes must coincide with substantial energy emission, offering a framework where information is encoded in vacuum fluctuations and long-range entanglement. A Gaussian-state-based uniqueness proof confirms the partner construction is essentially unique under the stated conditions.

Abstract

The partner mode with respect to a vacuum state for a given mode (like that corresponding to one of the thermal particles emitted by a black hole) is defined and calculated. The partner modes are explicitly calculated for a number of cases, in particular for the modes corresponding to a particle detector being excited by turn-on/turn-off transients, or with the thermal particles emitted by the accelerated mirror model for black hole evaporation. One of the key results is that the partner mode in general is just a vacuum fluctuation, and one can have the partner mode be located in a region where the state cannot be distinguished from the vacuum state by any series of local measurements, including the energy density. I.e., "information" (the correlations with the thermal emissions) need not be associated with any energy transport. The idea that black holes emit huge amounts of energy in their last stages because of all the information which must be emitted under the assumption of black-hole unitarity is found not necessarily to be the case.

On the partner particles for moving mirror radiation and black hole evaporation

TL;DR

This paper defines and constructs partner modes associated with Hawking-like radiation in black-hole and moving-mmirror setups. By enforcing purity of the Hawking+partner sector and a second condition that ties Hawking and partner creation/annihilation events, the authors show that partner modes can be nonlocal and even reside in regions locally indistinguishable from vacuum. They extend the construction to detectors and amplifiers, deriving explicit expressions for partner wavefunctions and showing that partners often carry no local energy despite carrying correlations with emitted quanta, with long tails and horizon-crossing behavior. The results challenge the notion that information released by black holes must coincide with substantial energy emission, offering a framework where information is encoded in vacuum fluctuations and long-range entanglement. A Gaussian-state-based uniqueness proof confirms the partner construction is essentially unique under the stated conditions.

Abstract

The partner mode with respect to a vacuum state for a given mode (like that corresponding to one of the thermal particles emitted by a black hole) is defined and calculated. The partner modes are explicitly calculated for a number of cases, in particular for the modes corresponding to a particle detector being excited by turn-on/turn-off transients, or with the thermal particles emitted by the accelerated mirror model for black hole evaporation. One of the key results is that the partner mode in general is just a vacuum fluctuation, and one can have the partner mode be located in a region where the state cannot be distinguished from the vacuum state by any series of local measurements, including the energy density. I.e., "information" (the correlations with the thermal emissions) need not be associated with any energy transport. The idea that black holes emit huge amounts of energy in their last stages because of all the information which must be emitted under the assumption of black-hole unitarity is found not necessarily to be the case.

Paper Structure

This paper contains 8 sections, 87 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Definition of Partner Particle
  3. Partners and detectors
  4. Partners and amplifiers
  5. Moving Mirror Radiation
  6. Partner Particles for Mirror thermal radiation
  7. Conclusions
  8. Uniqueness Proof

Figures (3)

  • Figure 1: The evaluation of $\left\{\hbox{\boldmath$\alpha$}|\hbox{\boldmath$\beta$}\right\}(E)$ for the trapezoidal coupling as a function of $ET$ with $\tau=1.2~T$. The zeros correspond to orthogonality and pure two mode squeezing.
  • Figure 2: The amplitude $\phi_P$ as a function of $t$.
  • Figure 3: The outgoing detected Hawking mode, its shape when traced back to the initial state, and its partner mode.