Spherically symmetric canonical quantum gravity

TL;DR

This paper presents a canonical quantization approach for spherically symmetric spacetimes using real-valued variables, ensuring anomaly-free quantum constraints, and explores how Loop Quantum Gravity modifications deform the space-time algebra.

Contribution

It introduces a new canonical quantization method with specific factor ordering, compares it with previous approaches, and analyzes the impact of Loop Quantum Gravity modifications on the algebra.

Findings

Quantum constraint algebra remains anomaly free with chosen factor ordering

Physical Hilbert space structure is consistent with previous models

Holonomy modifications deform the Dirac space-time algebra beyond effective approximations

Abstract

Canonical quantization of spherically symmetric space-times is carried out, using real-valued densitized triads and extrinsic curvature components, with specific factor ordering choices ensuring in an anomaly free quantum constraint algebra. Comparison with previous work [1] reveals that the resulting physical Hilbert space has the same form, although the basic canonical variables are different in the two approaches. As an extension, holonomy modifications from Loop Quantum Gravity are shown to deform the Dirac space-time algebra, while going beyond `effective' calculations.