Choosing the phase for the spin-weighted spheroidal functions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908907355504640 |
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| author | Cook, Gregory B. Wang, Xiyue |
| author_facet | Cook, Gregory B. Wang, Xiyue |
| contents | The spin-weighted spheroidal functions are the eigenfunctions of the angular Teukolsky equation. They are a generalization of the widely used spin-weighted spherical functions, and are extremely important in the area of black-hole perturbation theory. Like other special functions, they have an inherent phase ambiguity and need to be phase fixed to be uniquely defined. Clearly, such a phase choice does not have a direct physical impact. But, a poorly constructed phase choice could hinder the extraction, from mode information, of physical information about a system. To date, possible phase choices for the spin-weighted spheroidal functions have received little attention. Here, we clearly define and extensively explore two useful phase fixing schemes, and we propose that the spherical-limit phase-fixing scheme be adopted as the default phase-fixing scheme for the spin-weighted spheroidal functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22485 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Choosing the phase for the spin-weighted spheroidal functions Cook, Gregory B. Wang, Xiyue General Relativity and Quantum Cosmology The spin-weighted spheroidal functions are the eigenfunctions of the angular Teukolsky equation. They are a generalization of the widely used spin-weighted spherical functions, and are extremely important in the area of black-hole perturbation theory. Like other special functions, they have an inherent phase ambiguity and need to be phase fixed to be uniquely defined. Clearly, such a phase choice does not have a direct physical impact. But, a poorly constructed phase choice could hinder the extraction, from mode information, of physical information about a system. To date, possible phase choices for the spin-weighted spheroidal functions have received little attention. Here, we clearly define and extensively explore two useful phase fixing schemes, and we propose that the spherical-limit phase-fixing scheme be adopted as the default phase-fixing scheme for the spin-weighted spheroidal functions. |
| title | Choosing the phase for the spin-weighted spheroidal functions |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2603.22485 |