Researchers have formulated a theoretical framework for direct waves (DWs) in extreme-mass mergers, a type of gravitational signal arising from the interaction of a particle with a black hole. These waves, characterized by a complex frequency ωG, offer a unique window into the particle's orbital dynamics, including its motion within the ergosphere. The real part of ωG is influenced by the black hole's frame-dragging, while its imaginary part reflects the source's redshift, providing crucial information about the black hole's extreme environment.

Using the Green's function technique, the study describes how this frequency ωG is generated and how it is screened by the black hole's potential barrier. A connection is established between direct waves and dynamically excited quasinormal modes (QNMs). Furthermore, the long-term decay of DWs is predicted to follow the third-order horizon mode. To analyze these complex signals, a "pole-splitting method" is introduced, dividing the complete waveform into a QNM-pole sector and a non-QNM sector. Unlike traditional QNM filtering, which can distort the spectrum, this new method separates the contributions without altering the original signal.

Simulations of a quasi-circular plunge into a Kerr black hole with medium and rapid spins show that the frequency and decay rate of the non-pole sector in the dominant mode (ℓ = m = 2) evolve consistently with ωG, or its screened counterpart ωscreen. This finding validates direct waves as a sensitive tool for probing the ergosphere and redshift effects in the vicinity of black holes. The ability of these waves to directly probe the ergosphere opens new avenues for understanding physics in the most extreme regions of spacetime.