  New approach to exact solvability of dilaton gravity theories is suggested
which appeals directly to structure of field equations. It is shown that black
holes regular at the horizon are static and their metric is found explicitly.
If a metric possesses singularities the whole spacetime can be divided into
different sheets with one horizon on each sheet between neighboring
singularities with a finite value of dilaton field (addition horizons may arise
at infinite value of it), neighboring sheets being glued along the singularity.
The position of singularities coincide with the values of dilaton in solutions
with a constant dilaton field. Quantum corrections to the Hawking temperature
vanish. For a wide subset of these models the relationship between the total
energy and the total entropy of the quantum finite size system is the same as
in the classical limit. For another subset the metric itself does not acquire
quantum corrections. The present paper generalizes Solodukhin's results on the
RST model in that instead of a particular model we deal with whole classes of
them. Apart from this, the found models exhibit some qualitatively new
properties which are absent in the RST model. The most important one is that
there exist quantum black holes with geometry regular everywhere including
infinity.

High Energy Physics - Theory;General Relativity and Quantum Cosmology