BIRKHOFFS-THEOREM IN 2-DIMENSIONAL DILATON GRAVITY

The most general dilaton gravity theory in two spacetime dimensions is studied. It is proven that, up to spacetime diffeomorphisms, the gene ral solutions of the field equations form a one-parameter family of di stinct static solutions. It is explained how this result is consistent with a recent analysis showing that the reduced phase space for this class of theories is two dimensional. In particular, the second phase space degree of freedom is explicitly constructed in terms of spacetim e diffeomorphisms that cannot be generated canonically by local gauge transformations.