Asymptotic analysis of the EPRL model with timelike tetrahedra

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.