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We give the full list of types of static (homogeneous) solutions within a wide family of exactly solvable 2D dilaton gravities with the back-reaction of conformal fields. We discuss in detail the class of black hole solutions which includes the previously known ones as particular cases. For this class, the whole spacetime can be divided into dierent sheets with one horizon on each sheet between neighboring singularities with a finite value of dilaton field, the 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. We also consider a general approach to exactly solvable 2D dilaton cosmology. We find a rather rich class of everywhere regular solutions which exist practically in every type of the analyzed solutions. They exhibit dierent kinds of asymptotic behavior in the past and future, including inflation, superinflation, deflation, power expansion or contraction. In particular, for some models the dS spacetime with a time-dependent dilaton field is the exact solution of field equations. For some kinds of solutions the weak energy condition is violated independently of a specific model. We find also the solutions with a singularity which is situated in an infinite past (or future), so at any finite moment of a co-moving time the universe is singularity-free. It is pointed out that for some models the spacetime may be everywhere regular even in spite of infinitely large quantum back-reaction in an infinite past.

Exactly solvable models of 2D dilaton gravity