Loop quantum gravity of a spherically symmetric scalar field coupled to gravity with a clock

Abstract

The inclusion of matter fields in spherically symmetric loop quantum gravity has proved problematic at the level of implementing the constraint algebra including the Hamiltonian constraint. Here we consider the system with the introduction of a clock. Using the Abelianizaton technique we introduced in previous papers in the case of gravity coupled to matter, the system can be gauge fixed and rewritten in terms of a restricted set of dynamical variables that satisfy simple Poisson bracket relations. This creates a true Hamiltonian and therefore one bypasses the issue of the constraint algebra. We show how loop quantum gravity techniques may be applied for the vacuum case and show that the Hamiltonian system reproduces previous results for the physical space of states and the observables of a Schwarzchild black hole.

arXiv comment10 pages, RevTex, no figures, to appear in Classical and Quantum Gravity

References in corpus (6)

• Time and a physical Hamiltonian for quantum gravity
• Gravity quantized
• Scalar Material Reference Systems and Loop Quantum Gravity
• Quantum black holes in Loop Quantum Gravity
• Loop quantum black hole extensions within the improved dynamics
• Criticality in the collapse of spherically symmetric massless scalar fields in semi-classical loop quantum gravity

Cited by in corpus (2)

• Quantization of spherically symmetric loop quantum gravity coupled to a scalar field and a clock: the asymptotic limit
• Quantum scalar fields interacting with quantum black hole asymptotic regions