Spherically-symmetric geometries in a matter reference frame as quantum gravity condensate microstates

Candidate microstates of a spherically symmetric geometry are constructed in the group field theory formalism for quantum gravity, for models including both quantum geometric and scalar matter degrees of freedom. The latter are used as a material reference frame to define the spacetime localization of the various elements of quantum geometry. By computing quantum geometric observables, we then match the candidate quantum microstates with a spherically symmetric classical geometry, written in a suitable matter reference frame.