The paper looks at a recently identified feature of black‑hole merger radiation called the direct wave. Earlier work suggested that the direct wave’s oscillation frequency and its decay rate are tied to properties of the remnant black hole’s horizon — specifically the horizon frequency (a number set by the remnant spin and horizon radius) and the surface gravity (a measure related to how strongly the horizon pulls on nearby radiation). The authors test that claim using numerical relativity gravitational‑wave strain data and find the connection is not reliable.

The researchers isolated the direct wave from simulated merger signals using so‑called rational filters, a frequency‑domain tool designed to remove the usual quasinormal modes (QNMs). QNMs are the characteristic ringing tones of a perturbed black hole. They focused on the dominant (2,2) mode of the wave and modeled the filtered signal as a damped sinusoid, allowing either a fixed complex frequency or a time‑dependent complex frequency. They compared the real part of that frequency to twice the horizon frequency and the imaginary part (which sets the damping time) to the surface gravity.

Across a set of non‑precessing, quasi‑circular simulations from the SXS catalog, the authors found that the direct‑wave instantaneous frequency is relatively steady in time but does not track the horizon frequency except by coincidence near a remnant spin of about χf ≈ 0.7. That coincidence explains why some earlier studies saw agreement for the event GW250114, whose remnant spin happens to lie near that value. The decay rate, by contrast, evolves significantly on short timescales. In other words, a single damped sinusoid with a fixed damping time is not a good model for the direct wave.

They also tested an evolving‑frequency model that was explicitly built from horizon properties. That model can follow the direct wave in some moderate‑spin cases, but it fails for high remnant spins. As an example, for a high‑spin simulation with χf ≈ 0.95 the horizon‑based evolving model predicts the wrong oscillation frequency and does not reproduce the rapid evolution of the damping rate seen in the numerical data.