  We study a self-consistent solution of the semi-classical Einstein equation
including the back reaction from the Hawking radiation. Our geometry is
constructed by connecting flat space and the outgoing Vaidya metric at the
locus of the shock wave. In order to prove that this is the self-consistent
solution, we first show that the Weyl anomaly is canceled if we take the
effects of the fluctuations of the metric into account. We further demonstrate
that the Hawking radiation occurs even if the geometry has no horizon. Then,
the energy-momentum tensor is found to be consistent with the semi-classical
Einstein equation. Since our geometry has neither horizon nor singularity, all
matters inside the black hole finally come back to infinity. Therefore, no
information is lost by the black hole evaporation. Furthermore, we take into
account the gray-body factor. We construct a stationary solution for a black
hole in the heat bath and estimate the entropy. The entropy-area law is
reproduced by the volume integration of the entropy density over the inside of
the horizon, and the black hole can be treated as an ordinary thermodynamic
object.
