We show that the existence of semiclassical black holes of size as small as a
minimal length scale lUVā implies a bound on a gravitational analogue of
't-Hooft's coupling Ī»Gā(l)ā”N(l)GNā/l2 at all scales lā„lUVā. The proof is valid for any metric theory of gravity that consistently
extends Einstein's gravity and is based on two assumptions about semiclassical
black holes: i) that they emit as black bodies, and ii) that they are perfect
quantum emitters. The examples of higher dimensional gravity and of weakly
coupled string theory are used to explicitly check our assumptions and to
verify that the proposed bound holds. Finally, we discuss some consequences of
the bound for theories of quantum gravity in general and for string theory in
particular.Comment: 16 page