Perspectives on the dynamics in a loop quantum gravity effective description of black hole interiors

Abstract

In the loop quantum gravity context, there have been numerous proposals to quantize the reduced phase space of a black hole, and develop a classical effective description for its interior which eventually resolves the singularity. However, little progress has been made towards understanding the relation between such quantum/effective minisuperspace models and what would be the spherically symmetric sector of loop quantum gravity. In particular, it is not clear whether one can extract the phenomenological predictions obtained in minisuperspace models, such as the singularity resolution and the spacetime continuation beyond the singularity, based on results in full loop quantum gravity. In this paper, we present an attempt in this direction in the context of Kantowski-Sachs spacetime, through the proposal of two new effective Hamiltonians for the reduced classical model. The first is derived using Thiemann classical identities for the regularized expressions, while the second is obtained as a first approximation of the expectation value of a Hamiltonian operator in loop quantum gravity in a semi-classical state peaked on the Kantowski-Sachs initial data. We then proceed with a detailed analysis of the dynamics they generate and compare them with the Hamiltonian derived in General Relativity and the common effective Hamiltonian proposed in earlier literature.

13 pages, 2 figures; revised version accepted for publication in Phys. Rev. D

References in corpus (77)

• Background Independent Quantum Gravity: A Status Report
• Loop Quantum Cosmology: A Status Report
• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Nature of the Big Bang
• Real Ashtekar Variables for Lorentzian Signature Space-times
• Quantum Spin Dynamics (QSD)
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Loop Quantum Cosmology
• Quantum geometry and the Schwarzschild singularity
• A new spinfoam vertex for quantum gravity
• Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field
• Loop quantum black hole
• Isotropic Loop Quantum Cosmology
• Quantum Extension of the Kruskal Space-time
• Loop Quantum Dynamics of the Schwarzschild Interior
• Quantum Spin Dynamics (QSD) II
• Loop quantization of the Schwarzschild black hole
• Space-Time Structure of Loop Quantum Black Hole
• Disappearance of Black Hole Singularity in Quantum Gravity
• Gauge Field Theory Coherent States (GCS) : I. General Properties
• Gauge Field Theory Coherent States (GCS) : II. Peakedness Properties
• Loop Quantum Cosmology: An Overview
• Canonical Quantization of Spherically Symmetric Gravity in Ashtekar's Self-Dual Representation
• Homogeneous Loop Quantum Cosmology
• Algebraic Quantum Gravity (AQG) I. Conceptual Setup
• Black holes in loop quantum gravity: the complete space-time
• Spherically Symmetric Quantum Geometry: States and Basic Operators
• Loop quantization of the Schwarzschild interior revisited
• Coherent States for Canonical Quantum General Relativity and the Infinite Tensor Product Extension
• From black holes to white holes: a quantum gravitational, symmetric bounce
• Spherically Symmetric Quantum Geometry: Hamiltonian Constraint
• Alternative quantization of the Hamiltonian in loop quantum cosmology II: Including the Lorentz term
• Gauge Field Theory Coherent States (GCS) : III. Ehrenfest Theorems
• Quantum black holes in Loop Quantum Gravity
• Phenomenological loop quantum geometry of the Schwarzschild black hole
• Effective line elements and black-hole models in canonical (loop) quantum gravity
• Spherically Symmetric Gravity as a Completely Integrable System
• Cosmological Effective Hamiltonian from full Loop Quantum Gravity Dynamics
• Effective Quantum Extended Spacetime of Polymer Schwarzschild Black Hole
• Homogeneous Loop Quantum Cosmology: The Role of the Spin Connection
• Quantum Spin Dynamics (QSD) : VII. Symplectic Structures and Continuum Lattice Formulations of Gauge Field Theories
• Loop quantization of spherically symmetric midi-superspaces
• Black hole interior from loop quantum gravity
• Polymer Schwarzschild black hole: An effective metric
• Quantum-Reduced Loop Gravity: Cosmology
• Emergent de Sitter epoch of the quantum Cosmos
• Quantum gravity predictions for black hole interior geometry
• Loop quantization of spherically symmetric midi-superspaces : the interior problem
• Loop Quantum Cosmology III: Wheeler-DeWitt Operators
• Spinning Loop Black Holes
• Quantum resolution of black hole singularities
• Algebraic Quantum Gravity (AQG) II. Semiclassical Analysis
• Gauge-invariant coherent states for Loop Quantum Gravity I: Abelian gauge groups
• Non-singular black holes and the Limiting Curvature Mechanism: A Hamiltonian perspective
• New scalar constraint operator for loop quantum gravity
• Gauge-invariant coherent states for Loop Quantum Gravity II: Non-abelian gauge groups
• Hamiltonian operator for loop quantum gravity coupled to a scalar field
• Emergent de Sitter epoch of the Loop Quantum Cosmos: a detailed analysis
• Spherically symmetric Einstein-Maxwell theory and loop quantum gravity corrections
• Renormalization of symmetry restricted spin foam models with curvature in the asymptotic regime
• Quantum evolution of black hole initial data sets: Foundations
• Cosmological Coherent State Expectation Values in LQG I. Isotropic Kinematics
• Spherically symmetric sector of self dual Ashtekar gravity coupled to matter: Anomaly-free algebra of constraints with holonomy corrections
• Hamiltonian Renormalisation I: Derivation from Osterwalder-Schrader Reconstruction
• A curvature operator for LQG
• Signature change in 2-dimensional black-hole models of loop quantum gravity
• Quantum space-time of a charged black hole
• Covariance in self dual inhomogeneous models of effective quantum geometry: Spherical symmetry and Gowdy systems
• Coherent States for Black Holes
• Challenges in recovering a consistent cosmology from the effective dynamics of loop quantum gravity
• Black-hole horizons in modified space-time structures arising from canonical quantum gravity
• An introduction to spherically symmetric loop quantum gravity black holes
• Loop Quantum Corrected Einstein Yang-Mills Black Holes
• Stable coherent states
• On the polymer quantization of connection theories: graph coherent states
• Singularity Avoidance of Charged Black Holes in Loop Quantum Gravity
• Schrödinger-like quantum dynamics in loop quantized black holes

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• Shadow and Quasinormal Modes of a Rotating Loop Quantum Black Hole
• 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
• Spherically symmetric loop quantum gravity: analysis of improved dynamics
• Black hole collapse and bounce in effective loop quantum gravity
• (b,v)-type variables for black to white hole transitions in effective loop quantum gravity
• On the fate of quantum black holes
• Mass and Horizon Dirac Observables in Effective Models of Quantum Black-to-White Hole Transition
• Effective Dynamics from Coherent State Path Integral of Full Loop Quantum Gravity
• Bouncing compact objects I: Quantum extension of the Oppenheimer-Snyder collapse
• Constraints on the rotating self-dual black hole with quasi-periodic oscillations
• Properties of the spherically symmetric polymer black holes
• Improved Effective Dynamics of Loop-Quantum-Gravity Black Hole and Nariai Limit
• Bouncing compact objects. Part II: Effective theory of a pulsating Planck star
• Spherical symmetric gravitational collapse of a dust cloud: polymerized dynamics in reduced phase space
• Constraints on self-dual black hole in loop quantum gravity with S0-2 star in the Galactic Center
• Loop quantum black hole extensions within the improved dynamics
• Improved ($\bar{\mu }$-Scheme) Effective Dynamics of Full Loop Quantum Gravity
• Observational tests of the self-dual spacetime in loop quantum gravity
• Causal Structure of a recent Loop Quantum Gravity Black Hole Collapse Model
• Effective Quantum Dust Collapse via Surface Matching
• Observational tests of quantum extension of Schwarzschild spacetime in loop quantum gravity with stars in the galactic center
• Loop Quantum Gravity motivated multihorizon rotating black holes
• Understanding quantum black holes from quantum reduced loop gravity
• Annihilation-to-nothing: DeWitt boundary condition inside a black hole
• Revisiting quantum black holes from effective loop quantum gravity
• Particle dynamics and the accretion disk around a Self-dual Black Hole immersed in a magnetic field in Loop Quantum Gravity
• Loop effective model for Schwarzschild black hole interior: a modified $\bar{\mu }$ dynamics
• On the Possible Spacetime Structures of Rotating Loop Quantum Black Holes
• Trouble with geodesics in black-to-white hole bouncing scenarios
• Quantum geometry and black holes
• Generic features of a polymer quantum black hole
• Symmetry restriction and its application to gravity
• Effective LQC model for k=+1 isotropic cosmologies from spatial discretisations
• Dynamically implementing the $\overline{\mu }$-scheme in cosmological and spherically symmetric models in an extended phase space model
• On the Role of Fiducial Structures in Minisuperspace Reduction and Quantum Fluctuations in LQC
• Probing the interior of the Schwarzschild black hole using congruences: LQG vs. GUP
• Extended geometry of Gambini-Olmedo-Pullin polymer black hole and its quasinormal spectrum