Explain late-time QNM/tail amplitude comparability

Explain why amplitudes of quasi-normal modes and tail terms become comparable only at late times in BBH simulations—rather than shortly after merger—and determine whether this feature is tied to global boundary conditions such as the no-incoming-radiation condition at the horizon.

Background

Linear perturbations on Kerr backgrounds generically include normal modes, QNMs, and tails. Numerical relativity commonly observes late-time signals dominated by QNMs; tails appear to emerge much later, despite general expectations that tail amplitudes could compete earlier.

The review suggests this may be linked to global boundary conditions (e.g., no-incoming radiation at the horizon), and calls for a deeper theoretical account of the funneling of initial data into QNM-dominated regimes.

References

Open Issue 10 (OI-10) Why are the amplitudes comparable only at a late time such as \Sigma_0 rather than at earlier time \Sigma_1 soon after the merger? Is this feature also tied to a very global boundary condition such as `no incoming radiation' at $$?

— Quasi-Local Black Hole Horizons: Recent Advances  (2502.11825 - Ashtekar et al., 17 Feb 2025) in Section 6.2 (Remarks)

Nonetheless, because we do not currently have a full description of spheroidal harmonics for general large complex \omega, within the window the large-arc contribution is not understood. In this work in Kerr we still operationally set the split time to be |r_|+|r'_| as the Schwarzschild limit, and we leave the discussion of the exact split time to future studies.

— Gravitational Waves from Green's Function Decomposition for a Kerr black hole: I. Equatorial ISCO Plunge  (2608.17943 - Su et al., 18 Aug 2026) in Section 1, Introduction; Appendix E, Section 'Large-frequency angular reconstruction and the split time in Kerr'

A complete characterization of the very-late-time evolution and its horizon-controlled asymptote will require a more comprehensive model and is left to future work.

— Complex frequency evolution of direct waves from binary black hole mergers  (2608.23209 - Sun et al., 24 Aug 2026) in Section “Physical motivation for the direct wave,” subsection “Analytic approximation for a plunging particle”