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Wave function of the quantum black hole
High Energy Physics - Theory · Submitted 23 Feb 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The fact that the opening angle fluctuates away from its classical value of 2 pi indicates that the quantum black hole is a superposition of horizonless states.
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The abstract, sentence by sentence
We show that the Wald Noether charge entropy is canonically conjugate to the opening angle at the horizon. Using this canonical relation we extend the Wheeler-DeWitt equation to a Schroedinger equation in the opening angle, following Carlip and Teitelboim. We solve the equation in the semiclassical approximation by using the correspondence principle and find that the solutions are minimal uncertainty wavefunctions with a continuous spectrum for the entropy and therefore also of the area of the black hole horizon. The fact that the opening angle fluctuates away from its classical value of 2 pi indicates that the quantum black hole is a superposition of horizonless states. The classical geometry with a horizon serves only to evaluate quantum expectation values in the strict classical limit.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We show that the Wald Noether charge entropy is canonically conjugate to the opening angle at the horizon. | result 0.85 | 0.89 | 0.36 | asserted 1.00 |
| s1 | Using this canonical relation we extend the Wheeler-DeWitt equation to a Schroedinger equation in the opening angle, following Carlip and Teitelboim. | method 0.67 | 0.86 | 0.08 | asserted 1.00 |
| s2 | We solve the equation in the semiclassical approximation by using the correspondence principle and find that the solutions are minimal uncertainty wavefunctions with a continuous spectrum for the entropy and therefore also of the area of the black hole horizon. | result 0.96 | 0.95 | 0.46 | asserted 1.00 |
| s3 | The fact that the opening angle fluctuates away from its classical value of 2 pi indicates that the quantum black hole is a superposition of horizonless states. | interpretation 0.99 | 0.71 | 0.28 | hedged possibility 0.87 |
| s4 | The classical geometry with a horizon serves only to evaluate quantum expectation values in the strict classical limit. | interpretation 0.98 | 0.44 | 0.14 | asserted 1.00 |
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The paper
Original abstract
We show that the Wald Noether charge entropy is canonically conjugate to the opening angle at the horizon. Using this canonical relation we extend the Wheeler-DeWitt equation to a Schroedinger equation in the opening angle, following Carlip and Teitelboim. We solve the equation in the semiclassical approximation by using the correspondence principle and find that the solutions are minimal uncertainty wavefunctions with a continuous spectrum for the entropy and therefore also of the area of the black hole horizon. The fact that the opening angle fluctuates away from its classical value of 2 pi indicates that the quantum black hole is a superposition of horizonless states. The classical geometry with a horizon serves only to evaluate quantum expectation values in the strict classical limit.
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References
How the literature uses it
18 arXiv papers cite this in 38 sentences
Papers citing it · 29 sentences without a confident label
Uses its method or tool 4 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 $σ^2 = ħG/π$.
Restoring predictability in semiclassical gravitational collapse · Wavefunction of a semiclassical collapsing shell · 0.86
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In [ref] , we have proposed a concrete scheme for evaluating the semiclassical corrections using the wavefunction of [ref] .
Horizons of semiclassical black holes are cold · Introduction · 0.85
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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.
Firewalls, smoke and mirrors · Introduction · 0.97
Compares with it 1 paper
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We would also like to know if the emergent horizon fluctuates quantum mechanically and, if so, compare the strength of these fluctuations to that of previous works [ref] .
Emergent horizon, Hawking radiation and chaos in the collapsed polymer model of a black hole · Introduction · 0.97
Cites it as support 2 papers
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(For similar ideas, see [ref] .) The importance of accounting for a quantum fluctuating background may be contrary to expectations but has been explicitly shown to revise some of the standard premises of BH physics [ref] .
How Black Holes Burn · Introduction · 0.96
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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] .
Restoring predictability in semiclassical gravitational collapse · Introduction · 1.00
Cites it as background 1 paper
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Let us now review some of the relevant results from [ref] and put them in context.
Origin of the blackhole information paradox · Fluctuations of a bifurcating Killing horizon · 1.00
What it cites · 7 sentences without a confident label
Uses the method or tool of 2 papers
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Next we use Brown`s methods [ref] as applied in [ref] to show that the Lie derivative of the area of the $D-2$ hypersurface is canonically conjugate to the Wald entropy.
The Noether charge entropy in anti-deSitter space and its field theory dual · Introduction · 0.95
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Next we use Brown`s methods [ref] as applied in [ref] to show that the Lie derivative of the area of the $D-2$ hypersurface is canonically conjugate to the Wald entropy.
Gravitational entropy and thermodynamics away from the horizon · Introduction · 0.95
Cites as background 3 papers
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We refer to [ref] for the precise definitions of these quantities.
The Off-Shell Black Hole · Introduction · 0.97
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One contribution from infinity could be identified as the mass of the BH and another contribution from the horizon which Wald identified as the entropy of the BH [ref] .
Black Hole Entropy is Noether Charge · Introduction · 0.89
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One contribution from infinity could be identified as the mass of the BH and another contribution from the horizon which Wald identified as the entropy of the BH [ref] .
Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy · Introduction · 0.89
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