Hawking area law in quantum gravity

Abstract: We show that the LIGO--Virgo--KAGRA (LVK) verification of Hawking area law carries profound consequences for quantum gravity if such a law is postulated to hold exactly. The observed mergers can be produced in local Stelle gravity and in nonlocal quantum-gravity theories with entire or fractional form factors either by (i) singular Ricci-flat black holes or (ii) possibly regular classical black holes under very restrictive conditions: absence of $R^2$ and (Riemann)${}^2$ terms in the action, absence of extra real poles in the graviton propagator, and positivity of its spectral representation. To date, this is the strongest simplification of the ambiguities of this class of theories. We also prove that the classical standard black-hole entropy-area law holds as a consequence of Hawking area law, and provide a rigorous realization of Barrow's fractal black holes otherwise.