Unitary theory of evaporating two-dimensional black holes

We study a manifestly unitary formulation of two-dimensional dilaton quantum gravity based on the reduced phase space quantization. The spacetime metric operator can be expanded in a formal power series of the matter energy-momentum tensor operator. This expansion can be used for calculating quantum corrections to the classical black hole metric. This is done by evaluating the expectation value of the metric operator in an appropriate class of the physical states. When the normal ordering in the metric operator is chosen to be with respect to Kruskal vacuum, the lowest-order semiclassical metric is exactly the one-loop effective action metric discovered by Bose, Parker and Peleg. The corresponding semiclassical geometry describes an evaporating black hole which ends up as a remnant. The calculation of higher-order corrections and implications for the black hole fate are discussed.