A GENERALIZED UNCERTAINTY PRINCIPLE IN QUANTUM-GRAVITY

We discuss a Gedanken experiment for the measurement of the area of th e apparent horizon of a black hole in quantum gravity. Using rather ge neral and model-independent considerations we find a generalized uncer tainty principle which agrees with a similar result obtained in the fr amework of string theories. The result indicates that a minimum length of the order of the Planck length emerges naturally from any quantum theory of gravity, and that the concept of black hole is not operation ally defined if the mass is smaller than the Planck mass.