Nao Nakamoto | Searcharxiv

arXiv2026

Theoretical Aspects of Direct Waves in Kerr Black Holes: Pole-Splitting Method for Ringdown Analysis

We formulate the theoretical aspects of direct waves (DWs) in the case of extreme-mass merger. A DW is a source-driven waveform characterized by a complex frequency $ω_{\rm G}$, which reflects the orbital motion of the particle in the vicinity of the black hole, including a part of the orbit inside the ergoregion: its real part is governed by frame dragging and its imaginary part by the redshift of the source. Using the Green's function technique, we derive the source-driven frequency $ω_{\rm G}$, describe its screening by the potential barrier, and discuss its relation to dynamically excited quasinormal modes (QNMs). We then introduce a pole-splitting method that divides the full waveform into a QNM-pole sector and a non-QNM sector. Unlike QNM filtering, which multiplies the waveform spectrum by a filter function and thereby deforms it through a frequency-dependent time shift (i.e., group delay), our pole-splitting method merely divides the transfer function into pole and non-pole parts, separating the full waveform. Simulating a quasi-circular plunge into a Kerr black hole with medium and rapid spins, we find that the frequency and decay rate of the non-pole sector in the dominant mode, $\ell = m = 2$, evolve consistently with $ω_{\rm G}$-or with its screened counterpart $ω_{\rm screen}$-establishing the DW as a probe of the ergoregion and of the redshift effect around a black hole.

gr-qc↗

arXiv2026

Exceptional Lines and Excitation of (Nearly) Double-Pole Quasinormal Modes: A Semi-Analytic Study in the Nariai Black Hole

We show that quasinormal modes (QNMs) of a massive scalar field in Kerr-de Sitter and Myers-Perry black holes exhibit an exceptional line (EL), which is a continuous set of exceptional points (EPs) in parameter space, at which two QNM frequencies and their associated solutions coincide. We find that the EL appears in the parameter space spanned by the scalar mass and the black hole spin parameter, and also in the Nariai limit, i.e., $r_{\rm c} - r_{\rm h} \to 0$, where $r_{\rm c}$ and $r_{\rm h}$ denote the radii of the cosmological and black hole horizons, respectively. We analytically study the amplitudes or excitation factors of QNMs near the EL. Such an analytic treatment becomes possible since, in the Nariai limit, the perturbation equation reduces to a wave equation with the Pöschl-Teller (PT) potential. We discuss the destructive excitation of QNMs and the stability of the ringdown near and at the EL. The transient linear growth of QNMs -- a characteristic excitation pattern near an EP or EL -- together with the conditions under which this linear growth dominates the early ringdown, is also studied analytically. Our conditions apply to a broad class of systems that involve the excitation of (nearly) double-pole QNMs.

gr-qc↗