Black holes and gravitational thermodynamics

The 0-loop approximation for black-hole thermodynamics is applicable only when there are globally stable classical solutions to the corresponding boundary value problem. By including contributions from a specific class of non-classical geometries and by giving a measure for the path integral compatible with the classical limit, it has been possible to evaluate corrections to the partition function of the chi =2 topological sector, even when no classical solution exists. A density of states with very reasonable physical properties is also determined for this black-hole topology, consistent with earlier work.