The essential self-adjointness of the wave operator on radiative spacetimes
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908581483249664 |
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| author | Jia, Qiuye Molodyk, Mikhail Sussman, Ethan |
| author_facet | Jia, Qiuye Molodyk, Mikhail Sussman, Ethan |
| contents | We prove the essential self-adjointness of the d'Alembertian $\square_g$, allowing a larger class of spacetimes than previously considered, including those that arise from perturbing Minkowski spacetime by gravitational radiation. We emphasize the fact, proven by Taira in closely related settings, that all tempered distributions $u$ satisfying $\square_g u = λu +f$ for $λ\in \mathbb{C}\backslash \mathbb{R}$ and $f$ Schwartz are Schwartz. The proof is fully microlocal and relatively quick given the ``de,sc-'' machinery recently developed by the third author. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03828 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The essential self-adjointness of the wave operator on radiative spacetimes Jia, Qiuye Molodyk, Mikhail Sussman, Ethan Spectral Theory General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs Primary 35L05, 35P05. Secondary 58J47, 58J50 We prove the essential self-adjointness of the d'Alembertian $\square_g$, allowing a larger class of spacetimes than previously considered, including those that arise from perturbing Minkowski spacetime by gravitational radiation. We emphasize the fact, proven by Taira in closely related settings, that all tempered distributions $u$ satisfying $\square_g u = λu +f$ for $λ\in \mathbb{C}\backslash \mathbb{R}$ and $f$ Schwartz are Schwartz. The proof is fully microlocal and relatively quick given the ``de,sc-'' machinery recently developed by the third author. |
| title | The essential self-adjointness of the wave operator on radiative spacetimes |
| topic | Spectral Theory General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs Primary 35L05, 35P05. Secondary 58J47, 58J50 |
| url | https://arxiv.org/abs/2412.03828 |