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

A large class of solvable models of dilaton gravity in two space-time dimensions, capable of describing black hole geometry, is analyzed in a unified way as nonlinear \ensuremath{\sigma} models possessing a special symmetry. This symmetry, which can be neatly formulated in the target-space-covariant manner, allows one to decompose the nonlinearly interacting dilaton-gravity system into a free field and a field satisfying the Liouville equation with, in general, a nonvanishing cosmological term. In this formulation, all the existent models are shown to fall into the category with a vanishing cosmological constant. A general analysis of the space-time structure induced by a matter shock wave is performed and new models, with and without the cosmological term, are discussed.