Hamiltonian Thermodynamics of Charged Black Holes

We consider the most general diffeomorphism invariant action in 1+1 spacetime dimensions that contains a metric, dilaton and Abelian gauge field, and has at most second derivatives of the fields. Our action contains a topological term (linear in the Abelian field strength) that has not been considered in previous work. We impose boundary conditions appropriate for a charged black hole confined to a region bounded by a surface of fixed dilaton field and temperature. By making some simplifying assumptions about the quantum theory, the Hamiltonian partition function is obtained. This partition function is analyzed in some detail for the Reissner-Nordstrom black hole and for the rotating BTZ black hole.