Validate the direct-wave picture for comparable-mass mergers

Investigate whether the naive extension of the direct-wave picture developed for extreme-mass-ratio mergers can be validated for comparable-mass mergers.

Background

The paper develops a direct-wave description in the linear, extreme-mass-ratio regime, where a particle plunges into a Kerr black hole and the source-driven frequency is related to frame dragging and gravitational redshift. The authors explicitly restrict their analysis to this regime because extending the linear picture to comparable-mass mergers requires a more careful treatment.

The unresolved issue is whether the qualitative interpretation of direct waves—particularly their relation to the source trajectory, black-hole quantities, and the extraction of a non-quasinormal-mode component—remains valid when the binary has comparable masses and nonlinear effects become important.

References

Numerical-relativity waveforms have been used to extract the component from comparable-mass waveforms and to test its relation to $\Omega_{\rm H}$ and $\kappa$, although it is still non-trivial whether the naive extension of the picture of DW can be validated.

— Theoretical Aspects of Direct Waves in Kerr Black Holes: Pole-Splitting Method for Ringdown Analysis  (2609.11908 - Nakamoto et al., 10 Sep 2026) in Section 1, Introduction

We leave a quantitative explanation of these deviations to future work.

— Theoretical Aspects of Direct Waves in Kerr Black Holes: Pole-Splitting Method for Ringdown Analysis  (2609.11908 - Nakamoto et al., 10 Sep 2026) in Section 4, Conclusion