A bound on the effective gravitational coupling from semiclassical black holes

Understand

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-Hooft's coupling $\lambda_G(l)\equiv N(l) G_N/l^2$ at all scales $l \ge l_{UV}$.

• 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.