Canonical Structure of 2D Black Holes
  We determine the canonical structure of two-dimensional black-hole solutions arising in $2D$ dilaton gravity. By choosing the Cauchy surface appropriately we find that the canonically conjugate variable to the black hole mass is given by the difference of local (Schwarzschild) time translations at right and left spatial infinities. This can be regarded as a generalization of Birkhoff's theorem. 
J. Navarro-Salas, M. Navarro and C. F. Talavera