  Black holes formation and evolution have been extensively studied at the
classical level. However, not much is known regarding the end of their lives, a
phase that requires to consider the quantum nature of the gravitational field.
A black-to-white hole transition can capture the physics of this phenomenon, in
particular the physics of the residual small black holes at the end of the
Hawking evaporation. This work shows how the spin foam formalism is able to
describe this non-perturbative phenomenon. A thorough examination of the black
hole spacetime region in which quantum effects cannot be neglected indicates
that the scenario in which the black hole geometry undergoes a quantum
transition in a white hole geometry is natural and conservative. This quantum
transition is then studied using the spin foam formalism and the resulting
transition amplitude is explicitly computed.
