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 implementing constraint algebra including Hamiltonian constraint. Here we consider system with introduction a clock. Using abelianizaton technique introduced previous papers case coupled to matter, can be gauge fixed and rewritten terms restricted set dynamical variables that satisfy simple Poisson bracket relations. This creates true therefore one bypasses issue algebra. We show how techniques may applied for vacuum reproduces results physical space states observables Schwarzchild black hole.