Comment on "Superradiant stability of the Kerr black holes" (arXiv:1907.09118)
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918293727608832 |
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| author | Chen, Wen-Xiang |
| author_facet | Chen, Wen-Xiang |
| contents | We revisit the recent work of Huang on the superradiant stability of Kerr black holes coupled to massive scalar fields. While their analysis provides sufficient conditions for stability, it imposes an unnecessarily strong requirement by demanding that two roots of the relevant quartic equation be explicitly negative. By instead analyzing the polynomial's coefficients, we show that simpler constraints already exclude additional positive turning points, thereby slightly enlarging the region of guaranteed stability. We further present a near-extremal estimate that tightens the stability bound for rapidly spinning black holes. These refinements sharpen the analytic stability limits without introducing extra assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11787 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Comment on "Superradiant stability of the Kerr black holes" (arXiv:1907.09118) Chen, Wen-Xiang General Relativity and Quantum Cosmology We revisit the recent work of Huang on the superradiant stability of Kerr black holes coupled to massive scalar fields. While their analysis provides sufficient conditions for stability, it imposes an unnecessarily strong requirement by demanding that two roots of the relevant quartic equation be explicitly negative. By instead analyzing the polynomial's coefficients, we show that simpler constraints already exclude additional positive turning points, thereby slightly enlarging the region of guaranteed stability. We further present a near-extremal estimate that tightens the stability bound for rapidly spinning black holes. These refinements sharpen the analytic stability limits without introducing extra assumptions. |
| title | Comment on "Superradiant stability of the Kerr black holes" (arXiv:1907.09118) |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2601.11787 |