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PreprintCC BY 4.0arXiv

Symmetry preservation in black hole quasinormal mode spectra

  • Han-Wen Hu
  • Chen Lan
  • Zong-Kuan Guo
  • Rong-Gen Cai
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Abstract

We establish a general relation between symmetries of gravitational theories and black hole (BH) quasinormal mode (QNM) spectra. We show that a symmetry implies isospectrality when it induces a bijection between the corresponding QNM boundary value problems. However, conformally related BHs have been reported to exhibit both conformal factor dependent and independent QNM spectra. To resolve this issue, we develop a reduction scheme for higher order perturbation equations. Applied to pure Weyl gravity, it yields the complete axial spectrum of Schwarzschild, including Regge-Wheeler and spin-1 branches. Our results show that these seemingly contradictory conclusions result from differences in the perturbation dynamics or in the boundary conditions.

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Cite

BibTeXRIS
BibTeX
@misc{hu2026symmetry,
  title = {{Symmetry preservation in black hole quasinormal mode spectra}},
  author = {Han-Wen Hu and Chen Lan and Zong-Kuan Guo and Rong-Gen Cai},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18105},
  eprint = {2609.18105},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18105},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Symmetry preservation in black hole quasinormal mode spectra
AU  - Han-Wen Hu
AU  - Chen Lan
AU  - Zong-Kuan Guo
AU  - Rong-Gen Cai
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.18105
UR  - https://arxiv.org/abs/2609.18105
AB  - We establish a general relation between symmetries of gravitational theories and black hole (BH) quasinormal mode (QNM) spectra. We show that a symmetry implies isospectrality when it induces a bijection between the corresponding QNM boundary value problems. However, conformally related BHs have been reported to exhibit both conformal factor dependent and independent QNM spectra. To resolve this issue, we develop a reduction scheme for higher order perturbation equations. Applied to pure Weyl gravity, it yields the complete axial spectrum of Schwarzschild, including Regge-Wheeler and spin-1 branches. Our results show that these seemingly contradictory conclusions result from differences in the perturbation dynamics or in the boundary conditions.
ER  -