Callan-Giddings-Harvey-Strominger vacuum in loop quantum gravity and singularity resolution

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.

arXiv comment24 pages, 1 figure; v2: matches the PRD published version, titled modified according to the published version, a few typos corrected and a short comment regarding refined algebraic quantization added

References in corpus (31)

• Background Independent Quantum Gravity: A Status Report
• Loop Quantum Cosmology: A Status Report
• Quantum Nature of the Big Bang: Improved dynamics
• Evanescent Black Holes
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
• Dilaton Gravity in Two Dimensions
• Robustness of key features of loop quantum cosmology
• Loop quantum cosmology of k=1 FRW models
• Black hole evaporation: A paradigm
• Uniqueness of diffeomorphism invariant states on holonomy-flux algebras
• Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity
• Loop Quantum Dynamics of the Schwarzschild Interior
• Loop quantization of the Schwarzschild black hole
• Disappearance of Black Hole Singularity in Quantum Gravity
• Black holes in loop quantum gravity: the complete space-time
• Loop quantization of the Schwarzschild interior revisited
• Spherically Symmetric Quantum Geometry: Hamiltonian Constraint
• Quantum black holes in Loop Quantum Gravity
• Classical and Quantum Gravity in 1+1 Dimensions, Part I: A Unifying Approach
• Loop Quantization of Vacuum Bianchi I Cosmology
• Covariance in models of loop quantum gravity: Spherical symmetry
• Further Improvements in the Understanding of Isotropic Loop Quantum Cosmology
• Evaporation of 2-Dimensional Black Holes
• Dirac Constraint Quantization of a Dilatonic Model of Gravitational Collapse
• Quantum gravity effects in the CGHS model of collapse to a black hole
• Dilaton Gravity, Poisson Sigma Models and Loop Quantum Gravity
• New variables for 1+1 dimensional gravity
• Constraint Lie algebra and local physical Hamiltonian for a generic 2D dilatonic model
• Dirac Quantization of Two-Dimensional Dilaton Gravity Minimally Coupled to N Massless Scalar Fields
• A local true Hamiltonian for the CGHS model in new variables

Cited by in corpus (14)

• Spherically symmetric loop quantum gravity: analysis of improved dynamics
• Black hole singularity resolution via the modified Raychaudhuri equation in loop quantum gravity
• Signature change in 2-dimensional black-hole models of loop quantum gravity
• Signature change in loop quantum gravity: General midisuperspace models and dilaton gravity
• Linking loop quantum gravity quantization ambiguities with phenomenology
• Deformed algebra and the effective dynamics of the interior of black holes
• Path integral polymer propagator of relativistic and non-relativistic particles
• Effective GUP-modified Raychaudhuri equation and black hole singularity: four models
• Black hole interior quantization: a minimal uncertainty approach
• A generalized uncertainty-inspired quantum black hole
• Quantum fluctuating geometries and the information paradox
• Quantum fluctuating CGHS geometries and the information paradox
• A rotating GUP black hole: metric, shadow, and bounds on quantum parameters
• Probing the interior of the Schwarzschild black hole using congruences: LQG vs. GUP