Geometry Transition in Covariant Loop Quantum Gravity

Abstract

In this manuscript we present a calculation of a physical observable in a non-perturbative quantum gravitational physical process from covariant Loop Quantum Gravity. The process regards the transition of a trapped region to an anti--trapped region, treated as a quantum geometry transition akin to gravitational tunneling. Figuratively speaking, this is a quantum transition of a black hole to a white hole. The physical observables are the characteristic timescales in which the process takes place. After an introduction, we begin with two chapters that review, define and extend main tools relevant to Lorentzian spinfoams and their semiclassical limit. We then dedicate a chapter to the classical exterior spacetime, which provides the setup for the problem. In the last two chapters, we arrive at an explicit, analytically well-defined and finite expression for a transition amplitude describing this process and use the semiclassical approximation to estimate the relevant amplitudes for an arbitrary choice of boundary conditions. We conclude that the transition is predicted to be allowed by LQG, with a characteristic duration that is linear in the mass, when the process takes place. The probability for the process to take place is exponentially suppressed but non-zero, resulting to a long lifetime.