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Restoring predictability in semiclassical gravitational collapse
High Energy Physics - Theory · Submitted 14 May 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Here, we show that a semiclassical collapsing shell emits radiation that is only approximately thermal, with small but significant deviations.
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The abstract, sentence by sentence
Hawking showed that the radiation emitted from a classical collapsing shell is thermal. Here, we show that a semiclassical collapsing shell emits radiation that is only approximately thermal, with small but significant deviations. The most important difference is the presence of small off-diagonal elements in the radiation density matrix with a magnitude of order $1/\sqrt{S_{BH}}$, $S_{BH}$ being the Bekenstein-Hawking entropy of the incipient black hole. The off-diagonal elements store the correlations between the collapsing shell and the emitted radiation and allow information to continuously leak from the collapsed body. The rate of escape of information is initially very small, increasing to order one by the Page time, when the black hole has lost half its original entropy. We show that, until the Page time, the radiation is almost exactly thermal and that, from this time on, it begins to purify at an increasing rate.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Hawking showed that the radiation emitted from a classical collapsing shell is thermal. | background 1.00 | 0.02 | 0.02 | asserted 1.00 |
| s1 | Here, we show that a semiclassical collapsing shell emits radiation that is only approximately thermal, with small but significant deviations. | result 0.66 | 0.96 | 0.80 | asserted 1.00 |
| s2 | The most important difference is the presence of small off-diagonal elements in the radiation density matrix with a magnitude of order $1/\sqrt{S_{BH}}$, $S_{BH}$ being the Bekenstein-Hawking entropy of the incipient black hole. | result 1.00 | 0.89 | 0.29 | asserted 1.00 |
| s3 | The off-diagonal elements store the correlations between the collapsing shell and the emitted radiation and allow information to continuously leak from the collapsed body. | interpretation 0.93 | 0.82 | 0.30 | asserted 1.00 |
| s4 | The rate of escape of information is initially very small, increasing to order one by the Page time, when the black hole has lost half its original entropy. | result 0.99 | 0.85 | 0.13 | asserted 1.00 |
| s5 | We show that, until the Page time, the radiation is almost exactly thermal and that, from this time on, it begins to purify at an increasing rate. | result 0.99 | 0.95 | 0.34 | asserted 1.00 |
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The paper
Original abstract
Hawking showed that the radiation emitted from a classical collapsing shell is thermal. Here, we show that a semiclassical collapsing shell emits radiation that is only approximately thermal, with small but significant deviations. The most important difference is the presence of small off-diagonal elements in the radiation density matrix with a magnitude of order $1/\sqrt{S_{BH}}$, $S_{BH}$ being the Bekenstein-Hawking entropy of the incipient black hole. The off-diagonal elements store the correlations between the collapsing shell and the emitted radiation and allow information to continuously leak from the collapsed body. The rate of escape of information is initially very small, increasing to order one by the Page time, when the black hole has lost half its original entropy. We show that, until the Page time, the radiation is almost exactly thermal and that, from this time on, it begins to purify at an increasing rate.
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References
How the literature uses it
24 arXiv papers cite this in 65 sentences
Papers citing it · 52 sentences without a confident label
Builds on it 1 paper
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Then, following our earlier investigations [ref] , the multi-pair matrix is a $2 N_coh×2 N_coh$ matrix such that each entry is a block with the same dimensionality in frequency space as the one-pair matrix, $ρ_SC(ω,-ω ;N_T;N',N”)=ρ^1/2_H(ω,-ω) +Δρ_SC(ω,-ω ;N_T;N',N”)$.
Horizons of semiclassical black holes are cold · Multi-Pair density matrix · 0.80
Uses its method or tool 1 paper
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Following [ref] , we change variables to $Y=ω'-ω”$ and $Z=(ω'+ω”)/Y$ I(,δN) = ∫_0^∞d Y e^-Y^2/4C_BH(N_T) Y^-i2(ω-ω) e^- i Y C_BH()/2(N_T-) × [ ∫_1^∞dZ (Z+1)^-1/2-i2ω (Z-1)^-1/2+i2ω e^-i Y Z C_BH()/2 δN + ∫_1^∞dZ (Z-1)^-1/2-i2ω (Z+1)^-1/2+i2ω e^-i Y Z C_BH()/2 δN ] .
Phases of information release during black hole evaporation · Determining the Suppression Factor · 0.99
Uses its data or values 1 paper
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which was evaluated in [ref] to leading order in $C_BH$, ⟨ΔI_SC(C_BH) ⟩ = 1/2π C_BH e^-(ω'-ω”)^2/4 C_BH .
Phases of information release during black hole evaporation · Semiclassical density matrix · 0.92
Compares with it 2 papers
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This is also the reason why the first bit of information only comes out after the Page time, whereas the first bit emerges after the parametrically shorter time interval $t_coh$ in our framework [ref] .
How Black Holes Burn · Discussion: Pair-production perspective and comparison of models · 0.94
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It is interesting to compare the preceding calculation for $Tr[(ρ^(N_T)_OD)^2]$ with that of our earlier study [ref] .
Phases of information release during black hole evaporation · The rate of information transfer · 1.00
Cites it as background 8 papers
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The plan for the rest of the paper goes as follows: The subsequent section begins with a brief review of our previous results [ref] .
Horizons of semiclassical black holes are cold · Introduction · 0.92
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The semiclassical model [ref] improves upon Hawking's framework by taking into account the BH's quantum fluctuations, as well as its time dependence due to the emission of the radiation.
Density matrix of black hole radiation · The semiclassical model · 0.80
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For a non-exclusive reference of other recent approaches and arguments to find the origin of the problem see the papers [ref] .
On the Origin of Black Hole Paradoxes · Introduction · 0.96
What it cites · 16 sentences without a confident label
Uses the method or tool of 3 papers
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Adopting the the line of reasoning presented in [ref] (also see [ref] ), we can determine the proportionality constant such that $σ^2 = ħG/π$.
Wave function of the quantum black hole · Wavefunction of a semiclassical collapsing shell · 0.86
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Adopting the the line of reasoning presented in [ref] (also see [ref] ), we can determine the proportionality constant such that $σ^2 = ħG/π$.
Origin of the blackhole information paradox · Wavefunction of a semiclassical collapsing shell · 0.86
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Adopting the the line of reasoning presented in [ref] (also see [ref] ), we can determine the proportionality constant such that $σ^2 = ħG/π$.
Semiclassical black holes expose forbidden charges and censor divergent densities · Wavefunction of a semiclassical collapsing shell · 0.86
Cites as support 4 papers
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Another piece of supporting evidence was provided in [ref] , where it was shown that the horizon of a finite BH is subject to fluctuations due to the uncertainty principle and, as such, will have a degree of transparency that is missed in a perfectly classical treatment [ref] .
Black hole entropy divergence and the uncertainty principle · Introduction · 1.00
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Another piece of supporting evidence was provided in [ref] , where it was shown that the horizon of a finite BH is subject to fluctuations due to the uncertainty principle and, as such, will have a degree of transparency that is missed in a perfectly classical treatment [ref] .
Wave function of the quantum black hole · Introduction · 1.00
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Another piece of supporting evidence was provided in [ref] , where it was shown that the horizon of a finite BH is subject to fluctuations due to the uncertainty principle and, as such, will have a degree of transparency that is missed in a perfectly classical treatment [ref] .
Origin of the blackhole information paradox · Introduction · 1.00
Cites as background 13 papers
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(See also, e.g., [ref] .) This puzzle has attracted a recent surge of interest thanks, in large part, to a closely related conundrum that was first clarified in [ref] and is commonly known as the firewall paradox.
What Exactly is the Information Paradox? · Introduction · 0.97
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(See also, e.g., [ref] .) This puzzle has attracted a recent surge of interest thanks, in large part, to a closely related conundrum that was first clarified in [ref] and is commonly known as the firewall paradox.
Black Holes: Complementarity or Firewalls? · Introduction · 0.97
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For earlier papers that specifically consider horizon fluctuations, see [ref] .
Enhanced Black Hole Horizon Fluctuations · Introduction · 0.94
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