Andreas Blommaert (IAS) “Time in gravitational subregions and in closed universes”

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Abstract: I propose to construct gauge invariant local observables in subregions in quantum gravity by placing the operators at slices with fixed extrinsic curvature K, thus using K as a physical clock. This construction can be made precise in 2d JT gravity with conformal matter. The resulting set of gauge invariant observables form a type II von Nuemann algebra. This feature allows us to assign gravitational entropy to (states describing physics in) subregions. This construction works for closed universes where an observer has complete causal access, and in cases where an observer has restricted causal access (such as in the dS static patch or in more general FLRW cosmologies). An interesting question (which we do not answer) is whether the resulting entropy agrees with the gravitational path integral. Based on work with Chang-Han Chen.