2D black holes, conformal vacua and CFTs on the cylinder

We investigate two-dimensional dilaton gravity models with a power-law dilaton potential, whose black hole solutions contain, among others, the dimensional reduction of the Schwarzschild black hole, the anti-de Sitter black hole and Rindler spacetime. We show that the ground state of these models satisfies simple transformation laws under the SL(2,R) conformal group. We use these transformation laws to explain the scaling behavior of the thermodynamical parameters of the black hole and the nonextensivity of the thermodynamical system. The black hole thermodynamical behavior, in particular its entropy, is reproduced by a mapping into a two-dimensional conformal field theory on the cylinder.