  In this work we find static black hole solutions in the context of the
two-dimensional dilaton gravity, which is modified by the addition of an $R^2$
term. This term arises from the one-loop effective action of a massive scalar
field in its large mass expansion. The basic feature of this term is that it
does not contribute to the Hawking radiation of the classical black hole
backgrounds of the model. From this point of view a class of the solutions
derived are interpreted as describing backreaction effects. In particular it is
argued that evolution of a black hole via non-thermal signals is possible.
Nevertheless this evolution seems to be 'soft', in the sense that it does not
lead to the evaporation of a black hole, leaving the Hawking radiation as the
dominant mechanism for this process.
