Spherically Symmetric Quantum Geometry: Hamiltonian Constraint

TL;DR

This paper introduces variables for spherically symmetric quantum geometry that simplify the volume operator and enable explicit calculations of Hamiltonian constraints, supporting the consistency of loop quantum gravity in inhomogeneous models and advancing black hole physics.

Contribution

It develops a new set of variables for spherically symmetric models that streamline calculations and integrate seamlessly into loop quantum gravity, extending the framework to inhomogeneous situations.

Findings

Explicit matrix elements of Hamiltonian constraints computed

Supports consistency of loop quantum gravity in inhomogeneous models

Applications to black hole physics discussed

Abstract

Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and Lorentzian Hamiltonian constraints. The construction fits completely into the general scheme available in loop quantum gravity for the quantization of the full theory as well as symmetric models. This then presents a further consistency check of the whole scheme in inhomogeneous situations, lending further credence to the physical results obtained so far mainly in homogeneous models. New applications in particular of the spherically symmetric model in the context of black hole physics are discussed.