Black Holes from Within Loop Quantum Gravity

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In general relativity, the fields on a black hole horizon are obtained from those in the bulk by pullback and restriction. In quantum gravity, it would be natural to obtain them in the same manner. This is not fully realized in the quantum theory of isolated horizons in loop quantum gravity, in which a Chern-Simons phase space on the horizon is quantized separately from the bulk. I will outline an approach in which the quantum horizon degrees of freedom are simply components of the quantized bulk degrees of freedom. A condition is imposed on the quantum states to encode the existence of a horizon. I will present evidence that solutions to this condition have properties on the horizon that are remarkably similar to those of Chern-Simons theory. Instrumental in formulating the horizon condition are novel flux operators that use the Duflo isomorphism and seem to represent some type of quantum deformed SU(2). I will review their definition and summarize what I know about their properties.