  The dynamics of Liouville fields coupled to gravity are investigated by
applying the principle of general covariance to the Liouville action in the
context of a particular form of two-dimensional dilaton gravity. The resultant
field equations form a closed system for the Liouville/gravity interaction. A
large class of asymptotically flat solutions to the field equations is
obtained, many of which can be interpreted as black hole solutions. The
temperature of such black holes is proportional to their mass-parameters. An
exact solution to the back reaction problem is obtained to one-loop order, both
for conformally coupled matter fields and for the quantized metric/Liouville
system. Quantum effects are shown to map the space of classical solutions into
one another. A scenario for the end-point of black-hole radiation is discussed.
