On the interplay between the light ray and the magnetic X-ray transforms
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912222087741440 |
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| author | Oksanen, Lauri Paternain, Gabriel P. Sarkkinen, Miika |
| author_facet | Oksanen, Lauri Paternain, Gabriel P. Sarkkinen, Miika |
| contents | We study the light ray transform acting on tensors on a stationary Lorentzian manifold. Our main result is injectivity up to the natural obstruction as long as the associated magnetic vector field satisfies a finite degree property with respect to the vertical Fourier decomposition on the unit tangent bundle. This is based on an explicit relationship between the geodesic vector field of the Lorentzian manifold and the magnetic vector field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04061 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the interplay between the light ray and the magnetic X-ray transforms Oksanen, Lauri Paternain, Gabriel P. Sarkkinen, Miika Differential Geometry General Relativity and Quantum Cosmology Analysis of PDEs 35R30, 53C50, 53C65 We study the light ray transform acting on tensors on a stationary Lorentzian manifold. Our main result is injectivity up to the natural obstruction as long as the associated magnetic vector field satisfies a finite degree property with respect to the vertical Fourier decomposition on the unit tangent bundle. This is based on an explicit relationship between the geodesic vector field of the Lorentzian manifold and the magnetic vector field. |
| title | On the interplay between the light ray and the magnetic X-ray transforms |
| topic | Differential Geometry General Relativity and Quantum Cosmology Analysis of PDEs 35R30, 53C50, 53C65 |
| url | https://arxiv.org/abs/2502.04061 |