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A large class of solvable models of dilaton gravity in two space-timedimensions, capable of describing black hole geometry, are analyzed in aunified way as non-linear sigma models possessing a special symmetry. Thissymmetry, which can be neatly formulated in the target-space-covariant manner,allows one to decompose the non-linearly interacting dilaton-gravity systeminto a free field and a field satisfying the Liouville equation with in generalnon-vanishing cosmological term. In this formulation, all the existent modelsare shown to fall into the category with vanishing cosmological constant.General analysis of the space-time structureinduced by a matter shock wave isperformed and new models, with and without the cosmological term, arediscussed.Comment: 29 pages, LaTe

Unified approach to solvable models of dilaton gravity in two dimensions based on symmetry