In this article we study the Conrady-Hnybida extension of the Lorentzian Engle-Pereira-Rovelli-Livine spin-foam model, which admits timelike cells rather than just spacelike ones. Our focus is on the asymptotic analysis of the model’s vertex amplitude. We propose a new parametrization for states associated to timelike 3-cells, from which we derive a closed-form expression for their amplitudes. This allows us to revisit the conditions under which critical points of the amplitudes occur, and we find Regge-like geometrical critical points in agreement with the literature. However, we find also evidence for nongeometrical points which are not dynamically suppressed without further assumptions; the model then does not strictly asymptote to the Regge action, contrary to what one would expect. We moreover prove Minkowski and rigidity theorems for Minkowskian polyhedra, extending the asymptotic analysis to nonsimplicial spin-foams.

• Received 21 July 2021
• Accepted 13 October 2021

DOI:https://doi.org/10.1103/PhysRevD.104.126001