  We analyze quantum two dimensional dilaton gravity model, which is described
by $SL(2,R)/U(1)$ gauged Wess-Zumino-Witten model deformed by $(1,1)$ operator.
We show that the curvature singularity does not appear when the central charge
$c_{\rm matter}$ of the matter fields is given by $22<c_{\rm matter}<24$. When
$22<c_{\rm matter}<24$, the matter shock waves, whose energy momentum tensors
are given by $T_{\rm matter} \propto \delta(x^+ - x^+_0)$, create a kind of
wormholes, {\it i.e.,} causally disconnected regions. Most of the quantum
informations in past null infinity are lost in future null infinity but the
lost informations would be carried by the wormholes.
  We also discuss about the problem of defining the mass of quantum black
holes. On the basis of the argument by Regge and Teitelboim, we show that the
ADM mass measured by the observer who lives in one of asymptotically flat
regions is finite and does not vanish in general. On the other hand, the Bondi
mass is ill-defined in this model. Instead of the Bondi mass, we consider the
mass measured by observers who live in an asymptotically flat region at first.
A class of the observers finds the mass of the black hole created by a shock
wave changes as the observers' proper time goes by, i.e. they observe the
Hawking radiation. The measured mass vanishes after the infinite proper time
and the black hole evaporates completely. Therefore the total Hawking radiation
is positive even when $N<24$.
