Loop quantization of the Schwarzschild black hole

Abstract

We quantize spherically symmetric vacuum gravity without gauge fixing the diffeomorphism constraint. Through a rescaling, we make the algebra of Hamiltonian constraints Abelian and therefore the constraint algebra is a true Lie algebra. This allows the completion of the Dirac quantization procedure using loop quantum gravity techniques. We can construct explicitly the exact solutions of the physical Hilbert space annihilated by all constraints. New observables living in the bulk appear at the quantum level (analogous to spin in quantum mechanics) that are not present at the classical level and are associated with the discrete nature of the spin network states of loop quantum gravity. The resulting quantum space-times resolve the singularity present in the classical theory inside black holes.

4 pages, Revtex, version to appear in Physical Review Letters

References in corpus (7)

• Black Holes: Complementarity or Firewalls?
• Black hole evaporation: A paradigm
• Loop Quantum Dynamics of the Schwarzschild Interior
• Black holes in loop quantum gravity: the complete space-time
• Loop quantization of spherically symmetric midi-superspaces
• Loop quantization of spherically symmetric midi-superspaces : the interior problem
• Spherically symmetric Einstein-Maxwell theory and loop quantum gravity corrections

Cited by in corpus (147)

• An Apologia for Firewalls
• Planck stars
• Hořava Gravity at a Lifshitz Point: A Progress Report
• Loop quantization of the Schwarzschild interior revisited
• Editorial for the Special Issue 100 Years of Chronogeometrodynamics: The Status of the Einstein's Theory of Gravitation in Its Centennial Year
• From black holes to white holes: a quantum gravitational, symmetric bounce
• Testing loop quantum gravity from observational consequences of non-singular rotating black holes
• Classical collapse to black holes and quantum bounces: A review
• Tests of Loop Quantum Gravity from the Event Horizon Telescope Results of Sgr A${}^{\ast }$
• Quantum black holes in Loop Quantum Gravity
• Effective loop quantum gravity framework for vacuum spherically symmetric space-times
• Asymptotic safety casts its shadow
• Effective line elements and black-hole models in canonical (loop) quantum gravity
• Realistic Observable in Background-Free Quantum Gravity: the Planck-Star Tunnelling-Time
• 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
• Spherically symmetric loop quantum gravity: analysis of improved dynamics
• Geodesic completeness in a wormhole spacetime with horizons
• Polymer Schwarzschild black hole: An effective metric
• Black hole collapse and bounce in effective loop quantum gravity
• Quantum gravity of dust collapse: shock waves from black holes
• What is a singular black hole beyond General Relativity?
• From a locality-principle for new physics to image features of regular spinning black holes with disks
• Improved Black Hole Fireworks: Asymmetric Black-Hole-to-White-Hole Tunneling Scenario
• Hypersurface-deformation algebroids and effective space-time models
• Evidence for Maximal Acceleration and Singularity Resolution in Covariant Loop Quantum Gravity
• Excluding Black Hole Firewalls with Extreme Cosmic Censorship
• Towards conditions for black-hole singularity-resolution in asymptotically safe quantum gravity
• Kantowski-Sachs spacetime in loop quantum cosmology: bounds on expansion and shear scalars and the viability of quantization
• On effective loop quantum geometry of Schwarzschild interior
• Loop quantum Schwarzschild interior and black hole remnant
• Non-singular black holes and the Limiting Curvature Mechanism: A Hamiltonian perspective
• Image features of spinning regular black holes based on a locality principle
• Emergence of product of constant curvature spaces in loop quantum cosmology
• Perspectives on the dynamics in a loop quantum gravity effective description of black hole interiors
• Geodesic completeness and the lack of strong singularities in effective loop quantum Kantowski-Sachs spacetime
• Black hole singularity resolution via the modified Raychaudhuri equation in loop quantum gravity
• Asymptotic non-flatness of an effective black hole model based on loop quantum gravity
• Covariance in models of loop quantum gravity: Gowdy systems
• Quasinormal modes of a holonomy corrected Schwarzschild black hole
• Critical collapse of a scalar field in semiclassical loop quantum gravity
• Quantum signatures of black hole mass superpositions
• Inhomogeneities, loop quantum gravity corrections, constraint algebra and general covariance
• Sifting quantum black holes through the principle of least action
• Quantum evolution of black hole initial data sets: Foundations
• Loop quantum deparametrized Schwarzschild interior and discrete black hole mass
• Emergent modified gravity: Covariance regained
• Spherically symmetric sector of self dual Ashtekar gravity coupled to matter: Anomaly-free algebra of constraints with holonomy corrections
• Loop Quantum Gravity
• Signature change in 2-dimensional black-hole models of loop quantum gravity
• Bouncing compact objects. Part II: Effective theory of a pulsating Planck star
• Information loss, made worse by quantum gravity?
• Signature change in loop quantum gravity: General midisuperspace models and dilaton gravity
• Quantum Reduced Loop Gravity: a realistic Universe
• Linking loop quantum gravity quantization ambiguities with phenomenology
• Von-Neumann Stability and Singularity Resolution in Loop Quantized Schwarzschild Black Hole
• Breaking of isospectrality of quasinormal modes in nonrotating loop quantum gravity black holes
• Non-singular quantum gravitational dynamics of an LTB dust shell model: the role of quantization prescriptions
• An elementary introduction to loop quantum gravity
• Quantum space-time of a charged black hole
• Anomaly-free deformations of spherical general relativity coupled to matter
• Loop quantum black hole extensions within the improved dynamics
• Quantum-Reduced Loop-Gravity: Relation with the Full Theory
• Hawking radiation from a spherical loop quantum gravity black hole
• Quantum self-gravitating collapsing matter in a quantum geometry
• Gravitational axial perturbations and quasinormal modes of loop quantum black holes
• 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
• Quantum Black Hole Wave Packet: Average Area Entropy and Temperature Dependent Width
• Towards a quantum notion of covariance in spherically symmetric loop quantum gravity
• Brief review on black hole loop quantization
• The regular black hole in four dimensional Born-Infeld gravity
• Probing Quadratic Gravity with the Event Horizon Telescope
• An embedding of loop quantum cosmology in (b, v) variables into a full theory context
• Non-covariance of "covariant polymerization" in models of loop quantum gravity
• Loop quantization of the Gowdy model with local rotational symmetry
• Effective GUP-modified Raychaudhuri equation and black hole singularity: four models
• Emergence of string-like physics from Lorentz invariance in loop quantum gravity
• Quantum gravity lights up spinning black holes
• Holonomy and inverse-triad corrections in spherical models coupled to matter
• Rainbow Oppenheimer-Snyder collapse and the entanglement entropy production
• Constraining the loop quantum gravity parameter space from phenomenology
• Callan-Giddings-Harvey-Strominger vacuum in loop quantum gravity and singularity resolution
• Loop Quantum Gravity motivated multihorizon rotating black holes
• The connection between regular black holes in nonlinear electrodynamics and semi-classical dust collapse
• Annihilation-to-nothing: DeWitt boundary condition inside a black hole
• The Good, the Bad, and the Ugly of Gravity and Information
• Understanding quantum black holes from quantum reduced loop gravity
• A quantum reduction to spherical symmetry in loop quantum gravity
• Emergence of cosmic space and its connection with thermodynamic principles
• Effective Field Theory of Loop Quantum Cosmology
• Black holes in multi-fractional and Lorentz-violating models
• Scalar fields around a rotating loop quantum gravity black hole: Waveform, quasi-normal modes and superradiance
• Emergent modified gravity coupled to scalar matter
• Comment on "Towards a quantum notion of covariance in spherically symmetric loop quantum gravity"
• Symmetry Reduced Loop Quantum Gravity: A Bird's Eye View
• Constraint Lie algebra and local physical Hamiltonian for a generic 2D dilatonic model
• Quasinormal modes of a nonsingular spherically symmetric black hole effective model with holonomy corrections
• Ascribing quantum system to Schwarzschild spacetime with naked singularity
• Nonexistence of quantum black and white hole horizons in an improved dynamic approach
• Quasinormal modes of loop quantum black holes near the Planck scale
• Quantum-corrected Schwarzschild AdS black hole surrounded by quintessence: Thermodynamics and Shadows
• Geometry from Brackets Consistency
• Loop effective model for Schwarzschild black hole interior: a modified $\bar{\mu }$ dynamics
• No fermion doubling in quantum geometry
• Towards anisotropic cosmology in group field theory
• Spin foam amplitude of the black-to-white hole transition
• On the relation between reduced quantisation and quantum reduction for spherical symmetry in loop quantum gravity
• On the Possible Spacetime Structures of Rotating Loop Quantum Black Holes
• Decoding quantum gravity information with black hole accretion disk
• Quantum shells in a quantum space-time
• Can a false vacuum bubble remove the singularity inside a black hole?
• Space-time physics in background-independent theories of quantum gravity
• MONDified Gravity
• Scalar Quasi-Normal Modes of a Loop Quantum Black Hole
• Conformal loop quantum gravity coupled to the Standard Model
• Measuring the last burst of non-singular black holes
• Trouble with geodesics in black-to-white hole bouncing scenarios
• Numerical approach to the black-to-white hole transition
• Correlations across horizons in quantum cosmology
• Towards self dual Loop Quantum Gravity
• Quantum geometry and black holes
• Abelianized structures in spherically symmetric hypersurface deformations
• Relational dynamics and Page-Wootters formalism in group field theory
• Evolution in totally constrained models: Schrödinger vs. Heisenberg pictures
• Emergent modified gravity: Polarized Gowdy model on a torus
• Casimir effect in a quantum space-time
• Overdamped quasibound states inside a Schwarzschild black hole
• Schrödinger-like quantum dynamics in loop quantized black holes
• Algebraic backgrounds: a framework for noncommutative Kaluza-Klein theory
• Quantum vacuum effects on the final fate of a collapsing ball of dust
• Lessons for loop quantum gravity from emergent modified gravity
• Quantum Black Hole as a Harmonic Oscillator from the Perspective of the Minimum Uncertainty Approach
• Symplectic structure for general relativity and Einstein-Brillouin-Keller quantization
• Quantum correlation and origin of Hawking radiation for mass-superposed BTZ black holes
• Initiating the effective unification of black hole horizon area and entropy quantization with quasi-normal modes
• Spacetime Quanta? : The Discrete Spectrum of a Quantum Spacetime Four-Volume Operator in Unimodular Loop Quantum Cosmology
• Invariant Renormalization-Group improvement
• The ADM papers and part of their modern legacy: loop quantum gravity
• On anomaly freedom in spherically symmetric lattice loop quantization
• Connection Dynamics of Reduced 5-dimensional Kaluza-Klein Theory and Its Deparametrization
• Quantum effects of black holes and cosmological constant problem
• Probing the interior of the Schwarzschild black hole using congruences: LQG vs. GUP
• Black Holes as a Gateway to the Quantum: Classical and Semi-Classical Explorations
• Black-hole models in loop quantum gravity
• Does loop quantum ${\mu }_o$ scheme permit a black hole formation?