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-dimensional toy model given by dilaton gravity coupled to N massless scalar fields. After making the model well-defined by imposing reflecting boundary conditions at a critical value of the dilaton field, we quantize 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 further argue that in the semiclassical regime it describes the formation and subsequent Hawking evaporation of two-dimensional black holes. Finally, we note an interesting correspondence between the dilaton gravity S-matrix and that of the c = 1 matrix model.