Loop quantization of spherically symmetric midi-superspaces

2007/03/31 by Miguel Campiglia, Rodolfo Gambini, Jorge Pullin · 8 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc

paper · pdf · doi:10.1088/0264-9381/24/14/007

published as Class.Quant.Grav.24:3649-3672,2007 · 18 pages, RevTex, no figures, some typos corrected, published version, for some reason a series of figures were incorrectly added to the previous version

openalex publication_date 2007/07/04 · arxiv created 2008/05/08 · arxiv updated 2009/12/01 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/01

Abstract

We quantize the exterior of spherically symmetric vacuum spacetimes using a midi-superspace reduction within the Ashtekar new variables. Through a partial gauge fixing we eliminate the diffeomorphism constraint and are left with a Hamiltonian constraint that is first class. We complete the quantization in the loop representation. We also use the model to discuss the issues that will arise in more general contexts in the 'uniform discretization' approach to the dynamics.

Citations

• Algebraic quantum gravity (AQG): I. Conceptual setup
• Dirac-type approach for consistent discretizations of classical constrained theories
• Evolution without evolution: Dynamics described by stationary observables
• Spherically Symmetric Quantum Geometry: Hamiltonian Constraint
• Spherically Symmetric Quantum Geometry: States and Basic Operators
• On the superselection theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories

Cited by

• Loop quantization of the Schwarzschild black hole
• Schrödinger-like quantum dynamics in loop quantized black holes
• Phenomenological loop quantum geometry of the Schwarzschild black hole
• Semiclassical Loop Quantum Black Hole
• Emergent diffeomorphism invariance in a discrete loop quantum gravity model
• Quantum spacetime of a charged black hole
• Loop quantum dynamics of the Schwarzschild interior
• Quantum corrected spherical collapse: A phenomenological framework