Finite-information property of the effective merger S-matrix

Establish that, at every fixed order in the low-frequency expansion of black-hole merger waveforms, only a finite set of inclusive energy-flow, angular-momentum-flow, helicity-flow, and remnant-correlator observables is resolved, and determine the range of validity of this finite-information property against numerical-relativity waveforms.

Background

The effective merger SS-matrix program integrates out the strongly coupled merger region and represents its influence through inclusive observables describing radiated energy and angular momentum. At the order analyzed in the paper, recoil and nonlinear memory depend on a limited set of radiation moments, while higher orders are expected to involve connected multipoint energy-flow correlators and mixed correlators with remnant data. The authors formulate as a central conjecture that only finitely many such inclusive correlators are needed at any fixed order in the low-frequency expansion. Proving this would establish the effective merger construction as a systematic long-wavelength theory rather than merely an amplitude model.

References

The central conjecture of the effective merger S-matrix program is therefore that, to any fixed order in the low-frequency expansion, only a finite set of such inclusive correlators is resolved. Establishing this finite-information property and determining its range of validity against numerical-relativity waveforms would promote the construction from an amplitude model of merger into a genuine effective theory of strongly coupled gravitational dynamics viewed at long wavelengths.

— An Effective $S$-Matrix Approach to Low-Frequency Waveforms from Black Hole Mergers  (2609.10329 - Aoki et al., 9 Sep 2026) in Section 7, “Conclusions and outlook,” final paragraph