BOUNDARY DYNAMICS IN DILATON GRAVITY

We study the dynamics of the boundary in two-dimensional dilaton gravity coupled to N massless scalars. We rederive the boundary conditions of Refs. 1 and 3 in a way which makes the requirement of reparametrization invariance and the role of conformal anomaly explicit. We then study the semiclassical behavior of the boundary in the N = 24 theory in the presence of an incoming matter wave with a constant energy flux spread over a finite interval. There is a critical value of the matter energy density below which the boundary is stable and all the matter is reflected back. For energy densities greater than this critical value there is a similar behavior for small values of the total energy thrown in. However, when the total energy exceeds another critical value the boundary exhibits a runaway behavior and the space-time develops singularities and horizons.