The Robinson–Bueno Holographic Law: A Universal Mass–Ratio Scaling in Black–Hole Ringdowns

We report the discovery of a universal empirical scaling law governing deviations in the post-merger ringdown of binary black holes. Using a coherence-based, template-independent analysis of public LIGO–Virgo data, we identify a dimensionless holographic level n=C/C0n = C/C_0n=C/C0 that quantifies the strength of systematic departures from the classical Kerr ringdown prediction. We demonstrate that this quantity depends exclusively on the binary mass ratio q=M1/M2q = M_1/M_2q=M1/M2 and follows a robust power-law relation n(q)=a q−γn(q) = a\,q^{-\gamma}n(q)=aq−γ, holding continuously from near–equal–mass mergers to highly asymmetric systems such as GW190814 and GW190412. This scaling provides predictive power: once the mass ratio is determined during the inspiral, the expected magnitude of ringdown deviations is fixed a priori. The result establishes a new, testable link between gravitational-wave observations and the collective coherence of black-hole horizons.