  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.
