Comment on "On the bound states of the Schwarzschild black hole" by S. H. Völkel: A Reassessment of the Bound-State Analogy
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| Format: | Preprint |
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2025
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| _version_ | 1866918036865286144 |
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| author | Momeni, Davood |
| author_facet | Momeni, Davood |
| contents | This comment critically examines the recent proposal by S.~H.~Völkel [Phys. Rev. Lett., arXiv:2505.17186], which asserts that the quasinormal mode (QNM) spectrum of Schwarzschild black holes can be reconstructed from bound states of an inverted Regge--Wheeler potential. We demonstrate that this claim rests on a mathematically invalid spectral mapping and a misapplication of boundary conditions that define QNMs. Through a detailed figure-by-figure analysis, we expose deep inconsistencies in the numerical results and their physical interpretations. The inversion method, inspired by Mashhoon, is shown to fail in capturing the non-Hermitian, complex nature of black hole resonances. We contrast this with the rigorously established asymptotic structure of QNMs derived by Hod and others, concluding that the bound-state framework offers no reliable insight into black hole spectroscopy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_21836 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Comment on "On the bound states of the Schwarzschild black hole" by S. H. Völkel: A Reassessment of the Bound-State Analogy Momeni, Davood General Relativity and Quantum Cosmology High Energy Physics - Theory This comment critically examines the recent proposal by S.~H.~Völkel [Phys. Rev. Lett., arXiv:2505.17186], which asserts that the quasinormal mode (QNM) spectrum of Schwarzschild black holes can be reconstructed from bound states of an inverted Regge--Wheeler potential. We demonstrate that this claim rests on a mathematically invalid spectral mapping and a misapplication of boundary conditions that define QNMs. Through a detailed figure-by-figure analysis, we expose deep inconsistencies in the numerical results and their physical interpretations. The inversion method, inspired by Mashhoon, is shown to fail in capturing the non-Hermitian, complex nature of black hole resonances. We contrast this with the rigorously established asymptotic structure of QNMs derived by Hod and others, concluding that the bound-state framework offers no reliable insight into black hole spectroscopy. |
| title | Comment on "On the bound states of the Schwarzschild black hole" by S. H. Völkel: A Reassessment of the Bound-State Analogy |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2505.21836 |