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Quantum evolution of black hole initial data sets: Foundations

We construct a formalism for evolving spherically symmetric black hole initial data sets within a canonical approach to quantum gravity. This problem can be formulated precisely in quantum reduced loop gravity, a framework which has been successfully applied to give a full theory derivation of loop quantum cosmology. We extend this setting by implementing a particular choice of partial gauge which is then used to select a kinematical Hilbert space where the symmetry reduction is imposed through semiclassical states. The main result of this investigation is an effective Hamiltonian that can be used to solve for quantum black hole geometries by evolving classical black hole initial data sets.