Black to white hole transition in covariant loop quantum gravity

Covariant Loop Quantum Gravity (CLQG) is a promising tentative theory of quantum gravity that is background-independent and non-perturbative. One of the most intriguing aspects is the hypothetical transition from black to white holes, which could resolve classical singularities through quantum tunneling. This transition has been extensively studied in four Lorentzian dimensions, but the calculations are technically challenging and require numerous approximations. This thesis proposes an analogous model in a simplified three-dimensional Euclidean setting, enabling a deeper study of its mathematical structure, highlighting critical issues, and providing new interpretations of the results. New properties of coherent boundary states are identified, particularly their limitations in the context of usual tunneling processes and tunneling between geometries. Furthermore, we present, for the first time, an analytical and controlled form of the transition amplitude in CLQG. A transmission coefficient is also derived, and new insights into its interpretation are proposed. This thesis offers a formal, controlled, precise model to guide future theoretical developments.