The virtual black hole in 2d quantum gravity

As shown recently (W. Kummer, H. Liebl, D,V. Vassilevich, Nucl, Phys, B 544 (1999) 403) 2d quantum gravity theories - including spherically reduced Ei nstein-gravity - after an exact path integral of its geometric part can be treated perturbatively in the loops of (scalar) matter. Obviously the class ical mechanism of black hole formation should be contained in the tree appr oximation of the theory. This is shown to be the case for the scattering of two scalars through an intermediate state which by its effective black hol e mass is identified as a "virtual black hole". The present discussion is r estricted to minimally coupled scalers without and with mass. in the first case the probability amplitude diverges, except the black hole is "plugged" by a suitable boundary condition. For massive scalars a finite S-matrix el ement is obtained. (C) 2000 Elsevier Science B.V. All rights reserved.