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

Rodolfo GambiniJorge Pullin

Mar 2023

摘要

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

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