  The near-horizon geometry of evaporation black holes is determined according
to the semi-classical Einstein equation. We consider spherically symmetric
configurations in which the collapsing star has already collapsed below the
Schwarzschild radius. The back-reaction of the vacuum energy-momentum,
including Hawking radiation, is taken into account. The vacuum energy-momentum
plays a crucial role in a small neighborhood of the apparent horizon, as it
appears at the leading order in the semi-classical Einstein equation. Our study
is focused on the time-dependent geometry in this region.
