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We show that the existence of semiclassical black holes of size as small as aminimal length scale $l_{UV}$ implies a bound on a gravitational analogue of't-Hooft's coupling $\lambda_G(l)\equiv N(l) G_N/l^2$ at all scales $l \gel_{UV}$. The proof is valid for any metric theory of gravity that consistentlyextends Einstein's gravity and is based on two assumptions about semiclassicalblack holes: i) that they emit as black bodies, and ii) that they are perfectquantum emitters. The examples of higher dimensional gravity and of weaklycoupled string theory are used to explicitly check our assumptions and toverify that the proposed bound holds. Finally, we discuss some consequences ofthe bound for theories of quantum gravity in general and for string theory inparticular.

A bound on the effective gravitational coupling from semiclassical black holes