We show that the existence of semiclassical black holes of size as small as a minimal length scale $l_{UV}$ implies a bound on a gravitational analogue of t-Hoofts coupling $lambda_G(l)equiv N(l) G_N/l^2$ at all scales $l ge l_{UV}$. The proof is val
id for any metric theory of gravity that consistently extends Einsteins 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.
