Complete total-transmission modes of Kerr black holes
Abstract
We construct the complete spectrum of gravitational total-transmission modes (TTMs) of Kerr black holes and find four globally continuous families, n∞=1,2,3,4, each with two complex-conjugate frequency branches. Compared with the three-family classification of Cook and Lu, our global continuation resolves the mirror-related sectors of their n=2 family into separate families without introducing additional symmetry-unrelated roots. This organization distinguishes complex conjugation at fixed m from the mirror symmetry connecting the m and −m spectra. The n∞=3 family approaches the Schwarzschild algebraically special frequency, whereas the n∞=1,2, and $4$ families diverge as ω∝ a−4/3 along lower-half-plane directions −150∘, −90∘, and −30∘, respectively. High-precision data up to ℓ=32 confirm the Cook--Lu small-spin asymptotics and reveal how the divergent branches are embedded in the global four-family spectrum, with a family-dependent relation between the spherical-limit angular labels and the large-|aω| ordering. For axisymmetric perturbations, the n∞=2 and n∞=3 branches coalesce at genuine exceptional points, where the scattering spectral function develops a second-order zero and the TTM excitation factors are strongly enhanced, offering a different interpretation of the structure previously described by Cook and Lu as an overtone-multiplet splitting. Finally, we identify a previously unreported anomalous proximity between the n∞=3 TTM family and an unconventional Kerr quasinormal-mode sequence, with frequency separations reaching order 10−8 in the representative case studied.
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BibTeX
@misc{chen2026complete,
title = {{Complete total-transmission modes of Kerr black holes}},
author = {Changkai Chen and Xiaohua Zhang and Zhoujian Cao and Jiliang Jing and Sheng Long},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.39609},
eprint = {2609.39609},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39609},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Complete total-transmission modes of Kerr black holes
AU - Changkai Chen
AU - Xiaohua Zhang
AU - Zhoujian Cao
AU - Jiliang Jing
AU - Sheng Long
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.39609
UR - https://arxiv.org/abs/2609.39609
AB - We construct the complete spectrum of gravitational total-transmission modes (TTMs) of Kerr black holes and find four globally continuous families, n_∞=1,2,3,4, each with two complex-conjugate frequency branches. Compared with the three-family classification of Cook and Lu, our global continuation resolves the mirror-related sectors of their n=2 family into separate families without introducing additional symmetry-unrelated roots. This organization distinguishes complex conjugation at fixed m from the mirror symmetry connecting the m and −m spectra. The n_∞=3 family approaches the Schwarzschild algebraically special frequency, whereas the n_∞=1,2, and $4$ families diverge as ω∝ a^−4/3 along lower-half-plane directions −150^∘, −90^∘, and −30^∘, respectively. High-precision data up to ℓ=32 confirm the Cook--Lu small-spin asymptotics and reveal how the divergent branches are embedded in the global four-family spectrum, with a family-dependent relation between the spherical-limit angular labels and the large-|aω| ordering. For axisymmetric perturbations, the n_∞=2 and n_∞=3 branches coalesce at genuine exceptional points, where the scattering spectral function develops a second-order zero and the TTM excitation factors are strongly enhanced, offering a different interpretation of the structure previously described by Cook and Lu as an overtone-multiplet splitting. Finally, we identify a previously unreported anomalous proximity between the n_∞=3 TTM family and an unconventional Kerr quasinormal-mode sequence, with frequency separations reaching order 10^−8 in the representative case studied.
ER -