Using an argument due to Regge and Teitelboim, an expression for the ADM mass
of 2d quantum dilaton gravity is obtained. By evaluating this expression we
establish that the quantum theories which can be written as a Liouville-like
theory, have a lower bound to energy, provided there is no critical boundary.
This fact is then reconciled with the observation made earlier that the Hawking
radiation does not appear to stop. The physical picture that emerges is that of
a black hole in a bath of quantum radiation. We also evaluate the ADM mass for
the models with RST boundary conditions and find that negative values are
allowed. The Bondi mass of these models goes to zero for large retarded times,
but becomes negative at intermediate times in a manner that is consistent with
the thunderpop of RST.Comment: 16 pages, phyzzx, COLO-HEP-309. (Confusing points in previous version
clarified, discussion of ADM and Bondi masses in RST case added.
