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PreprintCC0arXiv

The (in)stability on total transmission modes with small bumps

  • Xi-Ning Dong
  • Liang-Bi Wu
  • Yu-Sen Zhou
  • Zong-Kuan Guo
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Abstract

Total transmission modes (TTMs) are a class of reflectionless solutions to black hole perturbation equations, closely related to quasinormal modes (QNMs), and can exhibit significant sensitivity to weak environmental perturbations. In this work, we investigate the spectrum (in)stability of TTMs of Tangherlini black holes by introducing a localized Pöschl-Teller bump perturbation into the effective potential, and employ a modified Chebyshev-Lobatto grid to improve the numerical accuracy of the localized perturbation. For d=14, ℓ=2, and s=2, the purely imaginary TTM exhibits relatively strong spectrum stability, whereas the genuine complex TTMs undergo significant migrations even for small perturbations, consistent with the spectrum stability revealed by previous pseudospectrum analyses.

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Cite

BibTeXRIS
BibTeX
@misc{dong2026instability,
  title = {{The (in)stability on total transmission modes with small bumps}},
  author = {Xi-Ning Dong and Liang-Bi Wu and Yu-Sen Zhou and Zong-Kuan Guo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07167},
  eprint = {2609.07167},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07167},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - The (in)stability on total transmission modes with small bumps
AU  - Xi-Ning Dong
AU  - Liang-Bi Wu
AU  - Yu-Sen Zhou
AU  - Zong-Kuan Guo
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07167
UR  - https://arxiv.org/abs/2609.07167
AB  - Total transmission modes (TTMs) are a class of reflectionless solutions to black hole perturbation equations, closely related to quasinormal modes (QNMs), and can exhibit significant sensitivity to weak environmental perturbations. In this work, we investigate the spectrum (in)stability of TTMs of Tangherlini black holes by introducing a localized Pöschl-Teller bump perturbation into the effective potential, and employ a modified Chebyshev-Lobatto grid to improve the numerical accuracy of the localized perturbation. For d=14, ℓ=2, and s=2, the purely imaginary TTM exhibits relatively strong spectrum stability, whereas the genuine complex TTMs undergo significant migrations even for small perturbations, consistent with the spectrum stability revealed by previous pseudospectrum analyses.
ER  -