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Callan-Giddings-Harvey-Strominger vacuum in loop quantum gravity and singularity resolution
General Relativity and Quantum Cosmology · Submitted 22 Aug 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim There, the eigenvalues of the dilaton and the metric operators cannot vanish locally, allowing us to conclude that singular geometries are ruled out in the quantum theory.
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The abstract, sentence by sentence
We study here a complete quantization of a Callan-Giddings-Harvey-Strominger (CGHS) vacuum model following loop quantum gravity techniques. Concretely, we adopt a formulation of the model in terms of a set of new variables that resemble the ones commonly employed in spherically symmetric loop quantum gravity. The classical theory consists of two pairs of canonical variables plus a scalar and diffeomorphism (first class) constraints. We consider a suitable redefinition of the Hamiltonian constraint such that the new constraint algebra (with structure constants) is well adapted to the Dirac quantization approach. For it, we adopt a polymeric representation for both the geometry and the dilaton field. On the one hand, we find a suitable invariant domain of the scalar constraint operator, and we construct explicitly its solution space. There, the eigenvalues of the dilaton and the metric operators cannot vanish locally, allowing us to conclude that singular geometries are ruled out in the quantum theory. On the other hand, the physical Hilbert space is constructed out of them, after group averaging the previous states with the diffeomorphism constraint. In turn, we identify the standard observable corresponding to the mass of the black hole at the boundary, in agreement with the classical theory. We also construct an additional observable on the bulk associated with the square of the dilaton field, with no direct classical analog.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study here a complete quantization of a Callan-Giddings-Harvey-Strominger (CGHS) vacuum model following loop quantum gravity techniques. | contribution 1.00 | 0.92 | 0.06 | asserted 0.91 |
| s1 | Concretely, we adopt a formulation of the model in terms of a set of new variables that resemble the ones commonly employed in spherically symmetric loop quantum gravity. | method 0.98 | 0.85 | 0.02 | asserted 1.00 |
| s2 | The classical theory consists of two pairs of canonical variables plus a scalar and diffeomorphism (first class) constraints. | background 0.74 | 0.17 | 0.03 | asserted 1.00 |
| s3 | We consider a suitable redefinition of the Hamiltonian constraint such that the new constraint algebra (with structure constants) is well adapted to the Dirac quantization approach. | method 0.96 | 0.91 | 0.03 | asserted 0.96 |
| s4 | For it, we adopt a polymeric representation for both the geometry and the dilaton field. | method 1.00 | 0.89 | 0.03 | asserted 0.99 |
| s5 | On the one hand, we find a suitable invariant domain of the scalar constraint operator, and we construct explicitly its solution space. | contribution 0.54 | 0.96 | 0.08 | asserted 1.00 |
| s6 | There, the eigenvalues of the dilaton and the metric operators cannot vanish locally, allowing us to conclude that singular geometries are ruled out in the quantum theory. | result 0.64 | 0.94 | 0.72 | asserted 1.00 |
| s7 | On the other hand, the physical Hilbert space is constructed out of them, after group averaging the previous states with the diffeomorphism constraint. | method 0.85 | 0.95 | 0.05 | asserted 1.00 |
| s8 | In turn, we identify the standard observable corresponding to the mass of the black hole at the boundary, in agreement with the classical theory. | result 0.72 | 0.94 | 0.08 | asserted 0.99 |
| s9 | We also construct an additional observable on the bulk associated with the square of the dilaton field, with no direct classical analog. | contribution 0.63 | 0.96 | 0.07 | asserted 1.00 |
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The paper
Original abstract
We study here a complete quantization of a Callan-Giddings-Harvey-Strominger (CGHS) vacuum model following loop quantum gravity techniques. Concretely, we adopt a formulation of the model in terms of a set of new variables that resemble the ones commonly employed in spherically symmetric loop quantum gravity. The classical theory consists of two pairs of canonical variables plus a scalar and diffeomorphism (first class) constraints. We consider a suitable redefinition of the Hamiltonian constraint such that the new constraint algebra (with structure constants) is well adapted to the Dirac quantization approach. For it, we adopt a polymeric representation for both the geometry and the dilaton field. On the one hand, we find a suitable invariant domain of the scalar constraint operator, and we construct explicitly its solution space. There, the eigenvalues of the dilaton and the metric operators cannot vanish locally, allowing us to conclude that singular geometries are ruled out in the quantum theory. On the other hand, the physical Hilbert space is constructed out of them, after group averaging the previous states with the diffeomorphism constraint. In turn, we identify the standard observable corresponding to the mass of the black hole at the boundary, in agreement with the classical theory. We also construct an additional observable on the bulk associated with the square of the dilaton field, with no direct classical analog.
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How the literature uses it
14 arXiv papers cite this in 22 sentences
Papers citing it · 11 sentences without a confident label
Uses its method or tool 1 paper
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At this point we follow [ref] and substitute the lapse and shift functions by [equation] where $F':=∂_x F=∂_+F+∂_-F$.
Quantum fluctuating CGHS geometries and the information paradox · Canonical formulation of CGHS's action · 0.99
Cites it as background 9 papers
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In LQG, there have been numerous works studying both the interior and the full spacetime of the Schwarzschild black hole [ref] .
Probing the interior of the Schwarzschild black hole using congruences: LQG vs. GUP · Introduction · 0.96
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In LQG, there have been extensive studies of both the interior [ref] and the full spacetime [ref] of the Schwarzschild black hole, as well as lower dimensional black holes mimicking the Schwarzschild full spacetime [ref] .
Black hole interior quantization: a minimal uncertainty approach · Introduction · 0.95
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They include models [ref] that treat the interior as a Kantowski-Sachs cosmology, the full spacetime [ref] , or further symmetry-reduced 2D systems [ref] .
A generalized uncertainty-inspired quantum black hole · Introduction · 0.95
What it cites · 25 sentences without a confident label
Builds on 2 papers
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The purpose of the present work is to put forward a quantization of the CGHS model, by extending the methods of [ref] to the case at hand.
Quantum black holes in Loop Quantum Gravity · Introduction · 0.99
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These two observables were first introduced for the 3+1 spherically symmetric case in [ref] and due to the similarities of the two models, we can see that they exist also for the CGHS model.
Loop quantization of the Schwarzschild black hole · Quantum observables · 0.97
Uses the method or tool of 6 papers
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In order to make things simpler, Gambini et. al. in [ref] take $η=1$ and since this is second class with the Gauss constraint, they can be solved to yield the final Hamiltonian [equation] sgn Int
Quantum black holes in Loop Quantum Gravity · Polar-type variables for spherically symmetric model · 0.87
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Furthermore, based on a proposal in Refs. [ref] , a redefinition of the scalar constraint is made, such that this constraint admits the standard algebra with the diffeomorphism constraint, while having a vanishing brackets with itself.
A local true Hamiltonian for the CGHS model in new variables · Introduction · 0.88
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Furthermore, based on a proposal in Refs. [ref] , a redefinition of the scalar constraint is made, such that this constraint admits the standard algebra with the diffeomorphism constraint, while having a vanishing brackets with itself.
Constraint Lie algebra and local physical Hamiltonian for a generic 2D dilatonic model · Introduction · 0.88
Cites as background 14 papers
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The CGHS model [ref] is a 2D dilatonic model.
Evanescent Black Holes · Brief review of the CGHS model · 1.00
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The application of LQG quantization techniques to simpler models, known as loop quantum cosmology (LQC), has dealt with the question of the resolution of the singularity at different levels in models similar to the one under study —see for instance Refs. [ref] among others—.
Loop Quantum Dynamics of the Schwarzschild Interior · Introduction · 0.81
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The application of LQG quantization techniques to simpler models, known as loop quantum cosmology (LQC), has dealt with the question of the resolution of the singularity at different levels in models similar to the one under study —see for instance Refs. [ref] among others—.
Evaporation of 2-Dimensional Black Holes · Introduction · 0.81
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