Spherically symmetric canonical quantum gravity

Abstract

Canonical quantization of spherically symmetric space-times is carried out, using real-valued densitized triads and extrinsic curvature components, with specific factor ordering choices ensuring in an anomaly free quantum constraint algebra. Comparison with previous work [1] reveals that the resulting physical Hilbert space has the same form, although the basic canonical variables are different in the two approaches. As an extension, holonomy modifications from Loop Quantum Gravity are shown to deform the Dirac space-time algebra, while going beyond `effective' calculations.

21 pages; minor corrections and additional references

References in corpus (15)

• Background Independent Quantum Gravity: A Status Report
• Geometrodynamics of Schwarzschild Black Holes
• Anomaly-free scalar perturbations with holonomy corrections in loop quantum cosmology
• Loop quantum gravity: an outside view
• Canonical Quantization of Spherically Symmetric Gravity in Ashtekar's Self-Dual Representation
• Spherically Symmetric Quantum Geometry: States and Basic Operators
• Spherically Symmetric Quantum Geometry: Hamiltonian Constraint
• Deformed General Relativity and Effective Actions from Loop Quantum Gravity
• An algebraic extension of Dirac quantization: Examples
• Discreteness corrections and higher spatial derivatives in effective canonical quantum gravity
• Unique determination of an inner product by adjointness relations in the algebra of quantum observables
• Effective constraint algebras with structure functions
• An algebraic approach to the quantization of cosntrained systems: finite dimensional examples
• Uniqueness of the Fock quantization of scalar fields and processes with signature change in cosmology
• Adjointness Relations as a Criterion for Choosing an Inner Product

Cited by in corpus (38)

• Covariance in models of loop quantum gravity: Spherical symmetry
• A consistent model of non-singular Schwarzschild black hole in loop quantum gravity and its quasinormal modes
• Critical evaluation of common claims in loop quantum cosmology
• Some implications of signature-change in cosmological models of loop quantum gravity
• Hypersurface-deformation algebroids and effective space-time models
• Black hole singularity resolution via the modified Raychaudhuri equation in loop quantum gravity
• Bouncing compact objects I: Quantum extension of the Oppenheimer-Snyder collapse
• Spherically symmetric sector of self dual Ashtekar gravity coupled to matter: Anomaly-free algebra of constraints with holonomy corrections
• Signature change in 2-dimensional black-hole models of loop quantum gravity
• Information loss, made worse by quantum gravity?
• Linking loop quantum gravity quantization ambiguities with phenomenology
• Loops rescue the no-boundary proposal
• Annihilation-to-nothing: a quantum gravitational boundary condition for the Schwarzschild black hole
• Covariance in self dual inhomogeneous models of effective quantum geometry: Spherical symmetry and Gowdy systems
• Non-covariance of the dressed-metric approach in loop quantum cosmology
• Deformed algebra and the effective dynamics of the interior of black holes
• Brief review on black hole loop quantization
• Effective GUP-modified Raychaudhuri equation and black hole singularity: four models
• Non-covariance of "covariant polymerization" in models of loop quantum gravity
• On the UV dimensions of Loop Quantum Gravity
• Anomaly freedom in perturbative models of Euclidean loop quantum gravity
• Constraining the loop quantum gravity parameter space from phenomenology
• Effective constraint algebras with structure functions
• Annihilation-to-nothing: DeWitt boundary condition inside a black hole
• Effective Field Theory of Loop Quantum Cosmology
• Rainbow-like Black Hole metric from Loop Quantum Gravity
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Deformed covariance in spherically symmetric vacuum models of loop quantum gravity: Consistency in Euclidean and self-dual gravity
• Inequivalence of mimetic gravity with models of loop quantum gravity
• Quasiclassical solutions for static quantum black holes
• Schrödinger-like quantum dynamics in loop quantized black holes
• Lessons for loop quantum gravity from emergent modified gravity
• On the geometry of no-boundary instantons in loop quantum cosmology
• Dynamically implementing the $\overline{\mu }$-scheme in cosmological and spherically symmetric models in an extended phase space model
• Quantization of the interior of the black hole
• Black hole or Fuzz ball or a Loop quantum star ? Assessing the fate of a massive collapsing star
• Singularity avoidance from path integral
• Black-hole models in loop quantum gravity