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 is used to probe several quantum gravity issues. In particular, it is found that if there is an electromagnetic wave of Planckian frequency even with such low amplitude that the curvature of the classical solution is small, the uncertainty in the quantum metric can be very large. More generally, the quantum fluctuations in the geometry are large unless the number and frequency of photons satisfy the inequality $N(ħG\omega {)}^2\ll 1$. Results hold also for a sector of the four-dimensional theory (consisting of Einstein-Rosen gravitational waves).