LARGE QUANTUM-GRAVITY EFFECTS - UNFORESEEN LIMITATIONS OF THE CLASSICAL-THEORY

Three-dimensional gravity coupled to Maxwell (or Klein-Gordon) fields is exactly soluble under the assumption of axisymmetry. The solution i s used to probe several quantum gravity issues. In particular, it is f ound that if there is an electromagnetic wave of Planckian frequency e ven with such low amplitude that the curvature of the classical soluti on is small, the uncertainty in the quantum metric can be very large. More generally, the quantum fluctuations in the geometry are large unl ess the number and frequency of photons satisfy the inequality N(hG om ega)(2) much less than 1. Results hold also for a sector of the four-d imensional theory (consisting of Einstein-Rosen gravitational waves).