The time evolution of black holes involves both the canonical equations of quantum gravity and the statistical mechanics of Hawking radiation, neither of which contains a time variable. In order to introduce the time, we apply the semiclassical approximation to the Hamiltonian constraint on the apparent horizon and show that, when the backreaction is included, it suggests the existence of a long-living remnant, similarly to what is obtained in the microcanonical picture for the Hawking radiation.Key words: black holes, Hawking effect, microcanonical ensemble, semiclassical approximation, quantum gravity PACS: 04.70.-s, 04.70.Dy, 04.60.-m A longstanding issue in theoretical physics is how to quantize Einstein gravity. Since in the theory there are constraints whose algebra contains structure functions (which depend on the space-time coordinates), one can conceive (inequivalent [1]) manners of lifting the Hamiltonian and momentum constraints to quantum equations, thus hindering the formal solution to the problem. On a more physical ground, one might notice that it is relevant to have a quantum theory of gravity at our disposal only for systems with very strong (Planck size) gravitational fields, such as those one expects in the early stages of the Universe. Because of Hawking's discovery of black hole evaporation [2], one also expect that quantum (or semiclassical) gravity plays a role in determining the dynamics of the late stages in the life of collapsed objects.In a general situation, one has to deal with the infinite number of degrees of freedom of the gravitational field configurations which are physically distinguished only modulo coordinate transformations. This gives the constraints the form of functional differential equations, for which there is little hope of finding general solutions, and one then tries to reduce the number of degrees 1