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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.Comment: 42 pages; v3: some typos fixe