Spherically symmetric loop quantum gravity: analysis of improved dynamics

Abstract

We study the "improved dynamics" for the treatment of spherically symmetric space-times in loop quantum gravity introduced by Chiou {\em et al.} in analogy with the one that has been constructed by Ashtekar, Pawlowski and Singh for the homogeneous space-times. In this dynamics the polymerization parameter is a well motivated function of the dynamical variables, reflecting the fact that the quantum of area depends on them. Contrary to the homogeneous case, its implementation does not trigger undesirable physical properties. We identify semiclassical physical states in the quantum theory and derive the corresponding effective semiclassical metrics. We then discuss some of their properties. Concretely, the space-time approaches sufficiently fast the Schwarzschild geometry at low curvatures. Besides, regions where the singularity is in the classical theory get replaced by a regular but discrete effective geometry with finite and Planck order curvature, regardless of the mass of the black hole. This circumvents trans-Planckian curvatures that appeared for astrophysical black holes in the quantization scheme without the improvement. It makes the resolution of the singularity more in line with the one observed in models that use the isometry of the interior of a Schwarzschild black hole with the Kantowski--Sachs loop quantum cosmologies. One can observe the emergence of effective violations of the null energy condition in the interior of the black hole as part of the mechanism of the elimination of the singularity.

arXiv comment26 pages, 8 figures

References in corpus (40)

• Loop Quantum Cosmology: A Status Report
• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Spin Dynamics (QSD)
• Robustness of key features of loop quantum cosmology
• Quantum geometry and the Schwarzschild singularity
• Quantum Transfiguration of Kruskal Black Holes
• Loop quantum black hole
• Quantum Extension of the Kruskal Space-time
• Loop Quantum Dynamics of the Schwarzschild Interior
• Loop quantization of the Schwarzschild black hole
• Loop quantization of the Schwarzschild interior revisited
• From black holes to white holes: a quantum gravitational, symmetric bounce
• Quantum black holes in Loop Quantum Gravity
• Cosmological Effective Hamiltonian from full Loop Quantum Gravity Dynamics
• Loop quantization of spherically symmetric midi-superspaces : the interior problem
• Quantum gravity predictions for black hole interior geometry
• Properties of a recent quantum extension of the Kruskal geometry
• Phenomenological dynamics of loop quantum cosmology in Kantowski-Sachs spacetime
• Prescriptions in Loop Quantum Cosmology: A comparative analysis
• 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
• 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
• Cosmological singularity resolution from quantum gravity: the emergent-bouncing universe
• Effective Dynamics from Coherent State Path Integral of Full Loop Quantum Gravity
• Mass and Angular Momentum in General Relativity
• Generalized boundary conditions for general relativity for the asymptotically flat case in terms of Ashtekar's variables
• The Evolution of $\Lambda$ Black Holes in the Mini-Superspace Approximation of Loop Quantum Gravity
• Quantum evolution of black hole initial data sets: Foundations
• Wave functions for the Schwarschild black hole interior
• Von-Neumann Stability and Singularity Resolution in Loop Quantized Schwarzschild Black Hole
• Hybrid Models in Loop Quantum Cosmology
• Quantum space-time of a charged black hole
• Quantum self-gravitating collapsing matter in a quantum geometry
• Interior metric and ray-tracing map in the firework black-to-white hole transition
• Brief review on black hole loop quantization
• Loop quantization of the Gowdy model with local rotational symmetry
• Quantum reduced loop gravity effective Hamiltonians from a statistical regularization scheme
• Callan-Giddings-Harvey-Strominger vacuum in loop quantum gravity and singularity resolution
• Classical axisymmetric gravity in real Ashtekar variables

Cited by in corpus (78)

• A Short Review of Loop Quantum Gravity
• Quantum Oppenheimer-Snyder and Swiss Cheese models
• Testing loop quantum gravity from observational consequences of non-singular rotating black holes
• Tests of Loop Quantum Gravity from the Event Horizon Telescope Results of Sgr A${}^{\ast }$
• Effective loop quantum gravity framework for vacuum spherically symmetric space-times
• Shadow and stability of quantum-corrected black holes
• An effective model for the quantum Schwarzschild black hole
• Black hole collapse and bounce in effective loop quantum gravity
• Quantum gravity of dust collapse: shock waves from black holes
• On the fate of quantum black holes
• On the geometry of the black-to-white hole transition within a single asymptotic region
• Black hole image encoding quantum gravity information
• Black hole singularity resolution via the modified Raychaudhuri equation in loop quantum gravity
• The End of a Black Hole's Evaporation -- Part I
• Properties of the spherically symmetric polymer black holes
• Gravitational lensing by a black hole in effective loop quantum gravity
• Improved Effective Dynamics of Loop-Quantum-Gravity Black Hole and Nariai Limit
• Spherical symmetric gravitational collapse of a dust cloud: polymerized dynamics in reduced phase space
• 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
• Loop quantum black hole extensions within the improved dynamics
• Causal Structure of a recent Loop Quantum Gravity Black Hole Collapse Model
• Deformed algebra and the effective dynamics of the interior of black holes
• Singularity resolution by holonomy corrections: Spherical charged black holes in cosmological backgrounds
• Effective four-dimensional loop quantum black hole with a cosmological constant
• Towards a quantum notion of covariance in spherically symmetric loop quantum gravity
• Effective Quantum Dust Collapse via Surface Matching
• Hamiltonian formulation and loop quantization of a recent extension of the Kruskal spacetime
• Painlevé-Gullstrand coordinates discontinuity in the quantum Oppenheimer-Snyder model
• Shell-crossings and shock formation during gravitational collapse in effective loop quantum gravity
• Reduced Phase Space Quantization of Black Holes: Path Integrals, and Effective Dynamics
• Effective GUP-modified Raychaudhuri equation and black hole singularity: four models
• Effective dynamics of the Schwarzschild black hole interior with inverse triad corrections
• A covariant polymerized scalar field in loop quantum gravity
• Developed Method. Interactions and their quantum picture
• Loop Quantum Gravity motivated multihorizon rotating black holes
• Finite-distance gravitational deflection of massive particles by a rotating black hole in loop quantum gravity
• Understanding quantum black holes from quantum reduced loop gravity
• Revisiting quantum black holes from effective loop quantum gravity
• Annihilation-to-nothing: DeWitt boundary condition inside a black hole
• Asymptotic flatness and Hawking quasilocal mass
• Birth of baby universes from gravitational collapse in a modified-gravity scenario
• Exploring alternatives to the Hamiltonian calculation of the Ashtekar-Olmedo-Singh black hole solution
• Extended phase space quantization of a black hole interior model in Loop Quantum Cosmology
• Two-time alternative to the Ashtekar-Olmedo-Singh black hole interior
• Black hole interior quantization: a minimal uncertainty approach
• Quasinormal modes of a nonsingular spherically symmetric black hole effective model with holonomy corrections
• Quasinormal modes of loop quantum black holes near the Planck scale
• Nonexistence of quantum black and white hole horizons in an improved dynamic approach
• Space of solutions of the Ashtekar-Olmedo-Singh effective black hole model
• Loop effective model for Schwarzschild black hole interior: a modified $\bar{\mu }$ dynamics
• On consistent gauge fixing conditions in polymerized gravitational systems
• A generalized uncertainty-inspired quantum black hole
• Axial perturbations in Kantowski-Sachs spacetimes and hybrid quantum cosmology
• Mass of cosmological perturbations in the hybrid and dressed metric formalisms of Loop Quantum Cosmology for the Starobinsky and exponential potentials
• Quasinormal modes of a charged loop quantum black hole
• On the Possible Spacetime Structures of Rotating Loop Quantum Black Holes
• Scalar Quasi-Normal Modes of a Loop Quantum Black Hole
• Trouble with geodesics in black-to-white hole bouncing scenarios
• Polar perturbations in Kantowski-Sachs spacetimes and hybrid quantum cosmology
• Loop Quantum Cosmology: Physics of Singularity Resolution and its Implications
• Quantum geometry and black holes
• Formation of nonsingular spherical black holes with holonomy corrections
• Generic features of a polymer quantum black hole
• Testing general covariance in effective models motivated by Loop Quantum Gravity
• Covariant effective spacetimes of spherically symmetric electrovacuum with a cosmological constant
• Radiative properties of a nonsingular black hole: Hawking radiation and gray-body factor
• Expansion operators in spherically symmetric loop quantum gravity
• Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives
• Dynamically implementing the $\overline{\mu }$-scheme in cosmological and spherically symmetric models in an extended phase space model
• Particle Deflections around Microscopic Loop Quantum Black Holes with Rigorous Quantum Parameters
• Nonsingular spherically symmetric black-hole model with holonomy corrections
• Connection Dynamics of Reduced 5-dimensional Kaluza-Klein Theory and Its Deparametrization
• Image of a quantum-corrected black hole without Cauchy horizons illuminated by a static thin accretion disk
• Formation of gravastars
• A loop quantization of the marginally bound Lemaître-Tolman-Bondi dust model
• Extended geometry of Gambini-Olmedo-Pullin polymer black hole and its quasinormal spectrum
• Probing the interior of the Schwarzschild black hole using congruences: LQG vs. GUP