Reduced Phase Space Quantization of Black Holes: Path Integrals, and Effective Dynamics

Abstract

We consider the loop quantum theory of the spherically symmetric model of gravity coupled to Gaussian dust fields, where the Gaussian dust fields provide a material reference frame of the space and time to deparameterize gravity. This theory, used to study the quantum features of the spherically symmetric black hole, is constructed based on a 1-dimensional lattice $\gamma \subset \mathbb{R}$. Taking advantage of the path integral formulation, we investigate the quantum dynamics and obtain an effective action. With this action, we get an effective continuous description of this quantum lattice system which is not the same as the one described by the effective Hamiltonian used in arXiv:2012.05729, i.e. the classical Hamiltonian with the holonomy correction. It turns out that the Hamiltonian derived in this paper returns that used in arXiv:2012.05729 only for macro black holes since the lattice $\gamma$ is required to be sufficiently fine. Indeed, it is necessary to propose this fine-grained lattice structure in order to well describe the underlying lattice theory by the continuous description.

arXiv comment26 pages, 6 figures, several key footnotes are added to clarify the derivation

References in corpus (49)

• Background Independent Quantum Gravity: A Status Report
• Discreteness of area and volume in quantum gravity
• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Theory of Gravity I: Area Operators
• LQG vertex with finite Immirzi parameter
• Loop Quantum Cosmology
• Quantum geometry and the Schwarzschild singularity
• Partial and Complete Observables for Hamiltonian Constrained Systems
• Loop quantum cosmology of Bianchi I models
• Quantum Transfiguration of Kruskal Black Holes
• Fundamental Structure of Loop Quantum Gravity
• Loop quantum black hole
• The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity
• Quantum Extension of the Kruskal Space-time
• Loop Quantum Dynamics of the Schwarzschild Interior
• The physical hamiltonian in nonperturbative quantum gravity
• Time and a physical Hamiltonian for quantum gravity
• Loop Quantum Cosmology: An Overview
• Spherically Symmetric Quantum Geometry: States and Basic Operators
• Loop quantization of the Schwarzschild interior revisited
• Algebraic Quantum Gravity (AQG) IV. Reduced Phase Space Quantisation of Loop Quantum Gravity
• From black holes to white holes: a quantum gravitational, symmetric bounce
• Gravity quantized
• Alternative quantization of the Hamiltonian in loop quantum cosmology II: Including the Lorentz term
• Scalar Material Reference Systems and Loop Quantum Gravity
• Reduced Phase Space Quantization and Dirac Observables
• Phenomenological loop quantum geometry of the Schwarzschild black hole
• Quantum black holes in Loop Quantum Gravity
• Cosmological Effective Hamiltonian from full Loop Quantum Gravity Dynamics
• Effective Quantum Extended Spacetime of Polymer Schwarzschild Black Hole
• Quantum Spin Dynamics VIII. The Master Constraint
• Spherically symmetric loop quantum gravity: analysis of improved dynamics
• Polymer Schwarzschild black hole: An effective metric
• Casting Loop Quantum Cosmology in the Spin Foam Paradigm
• Loop Quantum Cosmology and Spin Foams
• Loop quantum Schwarzschild interior and black hole remnant
• Effective Dynamics from Coherent State Path Integral of Full Loop Quantum Gravity
• Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings
• Hamiltonian operator for loop quantum gravity coupled to a scalar field
• Properties of the spherically symmetric polymer black holes
• Improved Effective Dynamics of Loop-Quantum-Gravity Black Hole and Nariai Limit
• Hamiltonian Renormalisation I: Derivation from Osterwalder-Schrader Reconstruction
• New Hamiltonian constraint operator for loop quantum gravity
• Bouncing evolution in a model of loop quantum gravity
• Deformed algebra and the effective dynamics of the interior of black holes
• An embedding of loop quantum cosmology in (b, v) variables into a full theory context
• Towards the self-adjointness of a Hamiltonian operator in loop quantum gravity
• Loop quantization of spherically symmetric midisuperspaces and loop quantum geometry of the maximally extended Schwarzschild spacetime
• State refinements and coarse graining in a full theory embedding of loop quantum cosmology

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• Effective four-dimensional loop quantum black hole with a cosmological constant
• Black holes and covariance in effective quantum gravity: A solution without Cauchy horizons
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• Covariant dynamics from static spherically symmetric geometries
• Covariant effective spacetimes of spherically symmetric electrovacuum with a cosmological constant
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