BLACK-HOLE FORMATION AND SPACE-TIME FLUCTUATIONS IN 2-DIMENSIONAL DILATON GRAVITY AND COMPLEMENTARITY

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