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Considerable attention has been paid to the study of the quantum geometry ofnonrotating black holes within the framework of Loop Quantum Cosmology. Thisinterest has been reinvigorated since the introduction of a novel effectivemodel by Ashtekar, Olmedo, and Singh. Despite recent advances in itsfoundation, there are certain questions about its quantization that stillremain open. Here we complete this quantization taking as starting point anextended phase space formalism suggested by several authors, including theproposers of the model. Adopting a prescription that has proven successful inLoop Quantum Cosmology, we construct an operator representation of theHamiltonian constraint. By searching for solutions to this constraint operatorin a sufficiently large set of dual states, we show that it can be solved for acontinuous range of the black hole mass. This fact seems in favour of aconventional classical limit (at least for large masses) and contrasts withrecent works that advocate a discrete spectrum. We present an algorithm thatdetermines the solutions in closed form. To build the corresponding physicalHilbert space and conclude the quantization, we carry out an asymptoticanalysis of those solutions, which allows us to introduce a suitable innerproduct on them.

Extended phase space quantization of a black hole interior model in Loop Quantum Cosmology