Integrable models and degenerate horizons in two-dimensional gravity

We analyze an integrable model of two-dimensional gravity which can be reduced to a pair of Liouville fields in the conformal gauge. Its general solution represents a pair of 'mirror' black holes with the same temperature. The ground state is a degenerate constant dilaton configuration similar to the Nariai solution of the Schwarzschild-de Sitter case. The existence of phi= const solutions and their relation to the solution given by the 2D Birkhoff theorem is then investigated in a more general context. We also point out some interesting features of the semiclassical theory of our model and the similarity with the behavior of AdS(2) black holes