Exceptional line and pseudospectrum in black hole spectroscopy
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| Format: | Preprint |
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2025
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| _version_ | 1866915630706327552 |
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| author | Cao, Li-Ming Ji, Ming-Fei Wu, Liang-Bi Zhou, Yu-Sen |
| author_facet | Cao, Li-Ming Ji, Ming-Fei Wu, Liang-Bi Zhou, Yu-Sen |
| contents | We investigate the exceptional points (EPs) and their pseudospectra in black hole perturbation theory. By considering a Gaussian bump modification to the Regge-Wheeler potential with variable amplitude, position, and width parameters, $(\varepsilon,d,σ_0)$, a continuous line of EPs (exceptional line, EL) in this three-dimensional parameter space is revealed. We find that the vorticity $ν=\pm1/2$ and the Berry phase $γ=π$ for loops encircling the EL, while $ν=0$ and $γ=0$ for those do not encircle the EL. Through matrix perturbation theory, we prove that the $ε$-pseudospectrum contour size scales as $ε^{1/q}$ at an EP, where $q$ is the order of the largest Jordan block of the Hamiltonian-like operator, contrasting with the linear $ε$ scaling at non-EPs. Numerical implements confirm this observation, demonstrating enhanced spectral instability at EPs for non-Hermitian systems including black holes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_17067 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exceptional line and pseudospectrum in black hole spectroscopy Cao, Li-Ming Ji, Ming-Fei Wu, Liang-Bi Zhou, Yu-Sen General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena Quantum Physics We investigate the exceptional points (EPs) and their pseudospectra in black hole perturbation theory. By considering a Gaussian bump modification to the Regge-Wheeler potential with variable amplitude, position, and width parameters, $(\varepsilon,d,σ_0)$, a continuous line of EPs (exceptional line, EL) in this three-dimensional parameter space is revealed. We find that the vorticity $ν=\pm1/2$ and the Berry phase $γ=π$ for loops encircling the EL, while $ν=0$ and $γ=0$ for those do not encircle the EL. Through matrix perturbation theory, we prove that the $ε$-pseudospectrum contour size scales as $ε^{1/q}$ at an EP, where $q$ is the order of the largest Jordan block of the Hamiltonian-like operator, contrasting with the linear $ε$ scaling at non-EPs. Numerical implements confirm this observation, demonstrating enhanced spectral instability at EPs for non-Hermitian systems including black holes. |
| title | Exceptional line and pseudospectrum in black hole spectroscopy |
| topic | General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena Quantum Physics |
| url | https://arxiv.org/abs/2511.17067 |