A bound on the effective gravitational coupling from semiclassical black holes

TL;DR

This paper establishes a universal bound on the effective gravitational coupling derived from properties of semiclassical black holes, with implications for quantum gravity and string theory.

Contribution

It introduces a bound on the gravitational 't-Hooft coupling based on black hole emission properties, valid across various metric theories of gravity.

Findings

The bound holds in higher-dimensional gravity and string theory.

Semiclassical black holes emit as perfect black bodies.

The bound constrains quantum gravity theories and string theory.

Abstract

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.