Spinfoam tunneling of quantum geometries in angle variables

Tunneling processes offer a promising path for finding signatures of quantum gravity. While tunneling of geometry has long been recognized in the literature, few detailed analyses in covariant loop quantum gravity have been carried out. We investigate spinfoam transitions in the holonomy representation, which naturally encodes the extrinsic curvature of boundary states. To reduce technical complications to a minimum, we study these amplitudes within the simple framework of the Ponzano-Regge spinfoam model for three-dimensional Euclidean quantum gravity. We identify the geometries dominating the spinfoam path integral in the classically forbidden regime when formulated in terms of dihedral angles as boundary data. We characterize these nonclassical geometries and show that their contributions to the spinfoam amplitude are exponentially suppressed in the semiclassical limit via analytic continuation of the discrete gravity action. We argue that they satisfy all the desired properties of tunneling processes. We also shed light on quantum black-to-white hole transitions, in particular clarifying the origin of the exponential suppression of various quantum amplitudes, while at the same time laying the basis for a future complete calculation of the amplitude in covariant loop quantum gravity.