  We construct a one-loop effective metric describing the evaporation phase of
a Schwarzschild black hole in a spherically symmetric null-dust model. This is
achieved by quantising the Vaidya solution and by chosing a time dependent
quantum state. This state describes a black hole which is initially in thermal
equilibrium and then the equilibrium is switched off, so that the black hole
starts to evaporate, shrinking to a zero radius in a finite proper time. The
naked singularity appears, and the Hawking flux diverges at the end-point.
However, a static metric can be imposed in the future of the end-point.
Although this end-state metric cannot be determined within our construction, we
show that it cannot be a flat metric.
