The Semi-Classical Limit of Quantum Gravity on Corners

We study quantum and classical systems associated with the quantum corner symmetry group $\mathrm{Q}\mathrm{C}\mathrm{S}=\widetilde{\mathrm{S}\mathrm{L}}(2,\mathbb{R})⋉{\mathrm{H}}_3,$ which arises in the context of quantum gravity. We relate quantum observables – specified by representation-theoretic data – to their classical counterparts using generalized Perelomov coherent states and the framework of Berezin quantization. This procedure links abstract representation-theoretic input to geometric classical observables, such as area. We conclude by applying the formalism to static, spherically symmetric spacetimes admitting a horizon.