Spectrum of the Laplacian on the Page metric
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866915081858580480 |
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| author | Hennigar, Robie A. Kunduri, Hari K. Sievers, Kam To Billy Wang, Yiqing |
| author_facet | Hennigar, Robie A. Kunduri, Hari K. Sievers, Kam To Billy Wang, Yiqing |
| contents | We numerically construct the spectrum of the Laplacian on Page's inhomogeneous Einstein metric on $\mathbb{CP}^2 \# \overline{\mathbb{CP}}^2$ by reducing the problem to a (singular) Sturm-Liouville problem in one dimension. We perform a perturbative analysis based upon a closely related, exactly solvable problem that strongly supports our results. We also study the spectrum of the Lichnerowicz Laplacian on symmetric traceless transverse two-tensors. The method relies on both the isometries of the Page metric and pseudospectral methods to numerically solve the resulting ODEs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19879 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectrum of the Laplacian on the Page metric Hennigar, Robie A. Kunduri, Hari K. Sievers, Kam To Billy Wang, Yiqing Spectral Theory General Relativity and Quantum Cosmology Mathematical Physics Differential Geometry We numerically construct the spectrum of the Laplacian on Page's inhomogeneous Einstein metric on $\mathbb{CP}^2 \# \overline{\mathbb{CP}}^2$ by reducing the problem to a (singular) Sturm-Liouville problem in one dimension. We perform a perturbative analysis based upon a closely related, exactly solvable problem that strongly supports our results. We also study the spectrum of the Lichnerowicz Laplacian on symmetric traceless transverse two-tensors. The method relies on both the isometries of the Page metric and pseudospectral methods to numerically solve the resulting ODEs. |
| title | Spectrum of the Laplacian on the Page metric |
| topic | Spectral Theory General Relativity and Quantum Cosmology Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2412.19879 |