CONFORMALLY INVARIANT BOUNDARY-CONDITIONS FOR DILATON GRAVITY

Quantum mechanical boundary conditions along a timelike line, correspo nding to the origin in radial coordinates, in two-dimensional dilaton gravity coupled to N matter fields, are considered. Conformal invarian ce and vacuum stability severely constrain the possibilities. The simp lest-choice found corresponds to a nonlinear Liouville-type boundary i nteraction. The scattering of low-energy matter off the boundary can b e computed perturbatively. It is found that weak incident pulses induc e damped oscillations at the boundary while large incident pulses prod uce black holes. The. response of the boundary to such pulses is semic lassically characterized by a second order, nonlinear ordinary differe ntial equation which is analyzed numerically.