Extended phase space quantization of a black hole interior model in Loop Quantum Cosmology

Abstract

Considerable attention has been paid to the study of the quantum geometry of nonrotating black holes within the framework of Loop Quantum Cosmology. This interest has been reinvigorated since the introduction of a novel effective model by Ashtekar, Olmedo, and Singh. Despite recent advances in its foundation, there are certain questions about its quantization that still remain open. Here we complete this quantization taking as starting point an extended phase space formalism suggested by several authors, including the proposers of the model. Adopting a prescription that has proven successful in Loop Quantum Cosmology, we construct an operator representation of the Hamiltonian constraint. By searching for solutions to this constraint operator in a sufficiently large set of dual states, we show that it can be solved for a continuous range of the black hole mass. This fact seems in favour of a conventional classical limit (at least for large masses) and contrasts with recent works that advocate a discrete spectrum. We present an algorithm that determines the solutions in closed form. To build the corresponding physical Hilbert space and conclude the quantization, we carry out an asymptotic analysis of those solutions, which allows us to introduce a suitable inner product on them.

16 pages

References in corpus (20)

• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Nature of the Big Bang
• Loop Quantum Dynamics of the Schwarzschild Interior
• Closed FRW model in Loop Quantum Cosmology
• From black holes to white holes: a quantum gravitational, symmetric bounce
• Hybrid quantization of an inflationary universe
• Phenomenological loop quantum geometry of the Schwarzschild black hole
• Loop Quantization of Vacuum Bianchi I Cosmology
• Physical evolution in Loop Quantum Cosmology: The example of vacuum Bianchi I
• Loop quantization of spherically symmetric midi-superspaces : the interior problem
• A no-go result for covariance in models of loop quantum gravity
• A Brief Introduction to Loop Quantum Cosmology
• The Quantum Configuration Space of Loop Quantum Cosmology
• The flat FRW model in LQC: the self-adjointness
• Wave functions for the Schwarschild black hole interior
• Breaking of isospectrality of quasinormal modes in nonrotating loop quantum gravity black holes
• Towards a quantum notion of covariance in spherically symmetric loop quantum gravity
• Hamiltonian formulation and loop quantization of a recent extension of the Kruskal spacetime
• Exploring alternatives to the Hamiltonian calculation of the Ashtekar-Olmedo-Singh black hole solution
• Two-time alternative to the Ashtekar-Olmedo-Singh black hole interior

Cited by in corpus (10)

• Black Holes and Covariance in Effective Quantum Gravity
• Absorption, Scattering, Geodesics, Shadows and Lensing Phenomena of Black Holes in Effective Quantum Gravity
• Revisiting quantum black holes from effective loop quantum gravity
• Axial perturbations in Kantowski-Sachs spacetimes and hybrid quantum cosmology
• Entangled pairs in evaporating black holes without event horizons
• Polar perturbations in Kantowski-Sachs spacetimes and hybrid quantum cosmology
• Master variables and Darboux symmetry for axial perturbations of the exterior and interior of black hole spacetimes
• On the evolution of the volume in Loop Quantum Cosmology
• Effective Regge-Wheeler equations of a hybrid loop quantum black hole
• Hamiltonian formalism, master functions and Darboux transformations for perturbed (interiors and exteriors of) nonrotating black holes