D. Louismartinez et G. Kunstatter, BIRKHOFFS-THEOREM IN 2-DIMENSIONAL DILATON GRAVITY, Physical review. D. Particles and fields, 49(10), 1994, pp. 5227-5230
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.