  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.
