Spherically symmetric systems of fields and black holes. IV. No room for black-hole evaporation in the reduced configuration space?

We investigate the question of whether and how the configuration space of the reduced system is restricted by the Hamiltonian constraint in the sense of Ashtekar and Horowitz. We deal with the model spherically symmetric system which has been defined and studied in the preceding papers of this series. We find restrictions of the asymptotical configuration space which seem to forbid the evaporation of black holes. Another consequence of the restrictions is that the relevant part of any spacetime with collapse can be foliated by Cauchy hypersurfaces so that the canonical formalism is applicable without problems. We show that singular apparent horizons can form, and that they are visible from the future null infinity, if the configuration space is not restricted. However, we are not able to construct the quantum field so that the results remain formal.