Quantization of spherically symmetric loop quantum gravity coupled to a scalar field and a clock: the asymptotic limit

We continue our work on the study of spherically symmetric loop quantum gravity coupled to two spherically symmetric scalar fields, one which acts as a clock. As a consequence of the presence of the latter, we can define a true Hamiltonian for the theory. The spherically symmetric context allows to carry out precise detailed calculations. Here we study the theory for regions of large values of the radial coordinate. This allows us to define in detail the vacuum of the theory and study its quantum states, yielding a quantum field theory on a quantum space time that makes contact with the usual treatment on classical space times.