Birkhoff's theorem in two-dimensional dilaton gravity

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Abstract
The most general dilaton gravity theory in two spacetime dimensions is studied. It is proven that, up to spacetime diffeomorphisms, the general solutions of the field equations form a one-parameter family of distinct 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 spacetime diffeomorphisms that cannot be generated canonically by local gauge transformations.

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