  A theory of quantum gravity is expected to change profoundly our
understanding of black holes. Quantum theory has already shown, as a first
approximation, that a black hole slowly evaporates. Non-perturbative quantum
gravity also predicts that such an object could metamorphose into a white hole,
its time-reverse. In this thesis, we study the foundations of such a scenario
and propose a mathematical model that includes the phenomenon of evaporation.
