A quantum S-matrix for two-dimensional black hole formation and evaporation (original) (raw)

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 derive the quantum S-matrix for the case that N=24. This S-matrix is unitary by construction, 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. * Note that in the spherically symmetric reduction of the Einstein theory, the line e −2φ = 0 coincides with the origin at r = 0 and indeed defines a reflecting boundary. † In [9] this vacuum energy was taken to be proportional to N-24. It will be shown later that (2.6) is the correct value, at least for N = 24.