Black hole formation and space-time fluctuations in two-dimensional dilaton gravity and complementarity

We study black hole formation in a model of two-dimensional dilaton gravity and 24 massless scalar fields with a boundary. We find the most general boundary condition consistent with perfect reflection of matter and constraints. We show that in the semiclassical approximation and for generic values of a parameter which characterizes the boundary conditions, the boundary starts receding to infinity at the speed of light whenever the total energy of the incoming matter flux exceeds a certain critical value. This is also the critical energy which marks the onset of black hole formation. We then compute the quantum fluctuations of the boundary and of the rescaled scalar curvature and show that as soon as the incoming energy exceeds this critical value, an asymptotic observer using normal time resolutions will always measure large quantum fluctuations of space-time near the horizon, even though the freely falling observer does not. This is an aspect of black hole complementarity relating directly to quantum gravity effects.