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Firewalls, smoke and mirrors
High Energy Physics - Theory · Submitted 7 Jan 2014
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim And so our previously proposed model which has $N_{coh}=S_{BH}^{1/2}$ is singled out.
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The abstract, sentence by sentence
The radiation emitted by a black hole (BH) during its evaporation has to have some degree of quantum coherence to accommodate a unitary time evolution. We parametrize the degree of coherence by the number of coherently emitted particles $N_{coh}$ and show that it is severely constrained by the equivalence principle. We discuss, in this context, the fate of a shell of matter that falls into a Schwarzschild BH. Two points of view are considered, that of a stationary external observer and that of the shell itself. From the perspective of the shell, the near-horizon region has an energy density proportional to $N_{coh}^2$ in Schwarzschild units. So, if $N_{coh}$ is parameterically larger than the square root of the BH entropy $S_{BH}^ {1/2}$, a firewall or more generally a "wall of smoke" forms and the equivalence principle is violated while the BH is still semiclassical. To have a degree of coherence that is parametrically smaller than $S_{BH}^{1/2}$, one has to introduce a new sub-Planckian gravitational length scale, which likely also violates the equivalence principle. And so our previously proposed model which has $N_{coh}=S_{BH}^{1/2}$ is singled out. From the external-observer perspective, we find that the time it takes for the information about the state of the shell to get re-emitted from the BH is inversely proportional to $N_{coh}$. When the rate of information release becomes order unity, the semiclassical approximation starts to break down and the BH becomes a perfect reflecting information mirror.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The radiation emitted by a black hole (BH) during its evaporation has to have some degree of quantum coherence to accommodate a unitary time evolution. | background 1.00 | 0.09 | 0.06 | asserted 0.83 |
| s1 | We parametrize the degree of coherence by the number of coherently emitted particles $N_{coh}$ and show that it is severely constrained by the equivalence principle. | contribution 0.52 | 0.93 | 0.15 | asserted 1.00 |
| s2 | We discuss, in this context, the fate of a shell of matter that falls into a Schwarzschild BH. | contribution 0.72 | 0.58 | 0.03 | unclear 0.70 |
| s3 | Two points of view are considered, that of a stationary external observer and that of the shell itself. | method 0.80 | 0.60 | 0.02 | asserted 0.76 |
| s4 | From the perspective of the shell, the near-horizon region has an energy density proportional to $N_{coh}^2$ in Schwarzschild units. | result 0.97 | 0.82 | 0.05 | asserted 1.00 |
| s5 | So, if $N_{coh}$ is parameterically larger than the square root of the BH entropy $S_{BH}^ {1/2}$, a firewall or more generally a "wall of smoke" forms and the equivalence principle is violated while the BH is still semiclassical. | result 0.92 | 0.80 | 0.34 | asserted 0.97 |
| s6 | To have a degree of coherence that is parametrically smaller than $S_{BH}^{1/2}$, one has to introduce a new sub-Planckian gravitational length scale, which likely also violates the equivalence principle. | result 0.89 | 0.77 | 0.09 | hedged possibility 0.93 |
| s7 | And so our previously proposed model which has $N_{coh}=S_{BH}^{1/2}$ is singled out. | result 0.57 | 0.63 | 0.55 | asserted 1.00 |
| s8 | From the external-observer perspective, we find that the time it takes for the information about the state of the shell to get re-emitted from the BH is inversely proportional to $N_{coh}$. | result 0.99 | 0.93 | 0.09 | asserted 1.00 |
| s9 | When the rate of information release becomes order unity, the semiclassical approximation starts to break down and the BH becomes a perfect reflecting information mirror. | result 0.83 | 0.83 | 0.20 | asserted 1.00 |
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The paper
Original abstract
The radiation emitted by a black hole (BH) during its evaporation has to have some degree of quantum coherence to accommodate a unitary time evolution. We parametrize the degree of coherence by the number of coherently emitted particles $N_{coh}$ and show that it is severely constrained by the equivalence principle. We discuss, in this context, the fate of a shell of matter that falls into a Schwarzschild BH. Two points of view are considered, that of a stationary external observer and that of the shell itself. From the perspective of the shell, the near-horizon region has an energy density proportional to $N_{coh}^2$ in Schwarzschild units. So, if $N_{coh}$ is parameterically larger than the square root of the BH entropy $S_{BH}^ {1/2}$, a firewall or more generally a "wall of smoke" forms and the equivalence principle is violated while the BH is still semiclassical. To have a degree of coherence that is parametrically smaller than $S_{BH}^{1/2}$, one has to introduce a new sub-Planckian gravitational length scale, which likely also violates the equivalence principle. And so our previously proposed model which has $N_{coh}=S_{BH}^{1/2}$ is singled out. From the external-observer perspective, we find that the time it takes for the information about the state of the shell to get re-emitted from the BH is inversely proportional to $N_{coh}$. When the rate of information release becomes order unity, the semiclassical approximation starts to break down and the BH becomes a perfect reflecting information mirror.
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References
How the literature uses it
9 arXiv papers cite this in 16 sentences
Papers citing it · 13 sentences without a confident label
Cites it as background 3 papers
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This so-called "firewall" has been discussed [ref] .
Thought Experiment to resolve the Black Hole Information Paradox · Introduction · 0.89
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The AMPS argument has elicited a large number of responses (including a few [ref] to forms of the argument realized even before the AMPS paper), some of which appear to support the firewall idea [ref] , others seem rather agnostic or ambivalent [ref] , and yet others of which raise skepticism about it [ref] .
Excluding Black Hole Firewalls with Extreme Cosmic Censorship · Introduction · 0.92
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For other work where various other corrections to the standard Hawking radiation picture are considered see, for example, [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] and [ref] .
Hawking radiation and secularly growing loop corrections · Introduction · 0.87
What it cites · 21 sentences without a confident label
Uses the method or tool of 7 papers
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We do this, following ideas from [ref] (also see [ref] as well as [ref] ), by endowing the collapsing shell with a wavefunction and calculating expectation values where appropriate.
Black hole entropy divergence and the uncertainty principle · Introduction · 0.97
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We do this, following ideas from [ref] (also see [ref] as well as [ref] ), by endowing the collapsing shell with a wavefunction and calculating expectation values where appropriate.
Black Hole's Quantum N-Portrait · Introduction · 0.97
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We do this, following ideas from [ref] (also see [ref] as well as [ref] ), by endowing the collapsing shell with a wavefunction and calculating expectation values where appropriate.
Wave function of the quantum black hole · Introduction · 0.97
Uses data or values from 1 paper
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The off-diagonal matrix $Δρ_OD(ω_out,ω_in)$ was calculated in [ref] and can be treated as a uniform matrix within the thermal window, when $ω_out$, $ω_in∼T_H$.
Horizons of semiclassical black holes are cold · Introduction · 0.84
Cites as background 22 papers
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The ensuing discussions revolve mostly around the various assumptions adopted by the original firewall proponents [ref] , which are based on the tenets of BH complementarity as expressed in [ref] .
Black Holes: Complementarity or Firewalls? · Introduction · 0.89
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The black hole (BH) information-loss paradox underscores the apparent violation of unitarity in the process of BH evaporation [ref] (for reviews, see [ref] ).
What Exactly is the Information Paradox? · Introduction · 0.96
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Hayden and Preskill (HP) answered this question [ref] for the Page model.
Black holes as mirrors: quantum information in random subsystems · Introduction · 0.83
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