A QUANTUM S-MATRIX FOR 2-DIMENSIONAL BLACK-HOLE FORMATION AND EVAPORATION

We study the black hole information paradox in the context of a two-di mensional toy model given by dilaton gravity coupled to N massless sca lar fields. After making the model well-defined by imposing reflecting boundary conditions at a critical value of the dilaton field, we quan tize the theory and define a quantum S-matrix for the case that N = 24 . This S-matrix maps pure initial states to pure out-states and we fur ther argue that in the semiclassical regime it describes the formation and subsequent Hawking evaporation of two-dimensional black holes. Fi nally, we note an interesting correspondence between the dilaton gravi ty S-matrix and that of the c = 1 matrix model.