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Abstract We study the asymptotic behaviour of the vertex amplitude for the EPRL spin foam model extended to include timelike tetrahedra. We analyze both, tetrahedra of signature −−− (standard EPRL), as well as of signature +−− (Hnybida–Conrady extension), in a unified fashion. However, we assume all faces to be of signature −−. We find that the critical points of the extended model are described again by 4-simplices and the phase of the amplitude is equal to the Regge action. Interestingly, in addition to the Lorentzian and Euclidean sectors there appear also split signature 4-simplices.
Kamiński et al. (Tue,) studied this question.