  The two-dimensional anti-de Sitter space(AdS_2) is constructed in terms of
the CGHS model. The geometric solutions are composed of the AdS vacuum and the
AdS black hole which are locally equivalent but distinguishable by their mass.
The infalling classical fields do not play any role but the quantum back
reaction is crucial in the formation of the AdS vacuum and AdS black hole. In
the presence of the AdS black hole, there does not exist any radiation, which
is consistent with the constraint equations. Therefore the transition from the
AdS black hole to the AdS vacuum is impossible, and they are quantum
mechanically stable . We discuss the reason why the vanishing Hawking radiation
appears in the AdS_2 black hole in contrast to asymptotically flat black holes.
