  We study analytically the spacetime geometry of the black-hole formation and
evaporation. As a simplest model of the collapse, we consider a spherical thin
shell, and take the back-reaction from the negative energy of the quantum
vacuum state. For definiteness, we will focus on quantum effects of s-waves. We
obtain an analytic solution of the semi-classical Einstein equation for this
model, that provides an overall description of the black hole geometry form the
formation to evaporation. As an application of this result, we find its
interesting implication that, after the collapsing shell enters the apparent
horizon, the proper distance between the shell and the horizon remains as small
as the Planck length even when the difference in their areal radii is of the
same order as the Schwarzschild radius. The position of the shell would be
regarded as the same place to the apparent horizon in the semi-classical regime
of gravity.
