  It is well known that spherically symmetric reduction of General Relativity
(SSG) leads to non-minimally coupled scalar matter. We generalize (and correct)
recent results to Hawking radiation for a class of dilaton models which share
with the Schwarzschild black hole non-minimal coupling of scalar fields and the
basic global structure. An inherent ambiguity of such models (if they differ
from SSG) is discussed. However, for SSG we obtain the rather disquieting
result of a negative Hawking flux at infinity, if the usual recipe for such
calculations is applied.
