Geometry transition in spinfoams

We show how the fixed-spin asymptotics of the EPRL model can be used to perform the spin-sum for spin foam amplitudes defined on fixed two-complexes without interior faces and contracted with coherent spin-network states peaked on a discrete simplicial geometry with macroscopic areas. We work in the representation given in (Han and Krajewski 2014 Class. Quantum Grav.31 01500). We first rederive the latter in a different way suitable for our purposes. We then extend this representation to 2-complexes with a boundary and derive its relation to the coherent state representation. We give the measure providing the resolution of the identity for Thiemann’s state in the twisted geometry parametrization. We then piece together these with other results in the literature and show how the spin sum can be performed analytically using the model asymptotics. These results are relevant to analytic investigations regarding the transition of a black hole to a white hole geometry. In particular, this work was the basis of the calculation presented in Christodoulou and D’Ambrosio (2018 (arXiv:1801.03027)).