Evanescent black holes

A renormalizable theory of quantum gravity coupled to a dilaton and conformal matter in two spacetime dimensions is analyzed. The theory is shown to be exactly solvable classically. Included among the exact classical solutions are configurations describing the formation of a black hole by collapsing matter. The problem of Hawking radiation and back reaction of the metric is analyzed to leading order in a $\frac{1}{N}$ expansion, where $N$ is the number of matter fields. The results suggest that the collapsing matter radiates away all of its energy before an event horizon has a chance to form, and black holes thereby disappear from the quantum-mechanical spectrum. It is argued that the matter asymptotically approaches a zero-energy "bound state" which can carry global quantum numbers and that a unitary $S$ matrix including such states should exist.