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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2205.05860 |
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| _version_ | 1866909386879795200 |
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| author | Eskin, Gregory |
| author_facet | Eskin, Gregory |
| contents | We study the Lorentzian metric independent of the time variable in the cylinder $\mathbb{R}\timesΩ$ where $x_0\in\mathbb{R}$ is the time variable and $Ω$ is a bounded smooth domain in $\mathbb{R}^n$. We consider forward null-geodesics in $\mathbb{R}\times Ω$ starting on $\mathbb{R}\times\partialΩ$ at $t=0$ and leaving $\mathbb{R}\timesΩ$ at some later time. We prove the following rigidity result: If two Lorentzian metrics are close enough in some norm and if corresponding null-geodesics have equal lengths then the metrics are equal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_05860 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Rigidity for Lorentzian metrics with the same length of null-geodesics Eskin, Gregory Analysis of PDEs We study the Lorentzian metric independent of the time variable in the cylinder $\mathbb{R}\timesΩ$ where $x_0\in\mathbb{R}$ is the time variable and $Ω$ is a bounded smooth domain in $\mathbb{R}^n$. We consider forward null-geodesics in $\mathbb{R}\times Ω$ starting on $\mathbb{R}\times\partialΩ$ at $t=0$ and leaving $\mathbb{R}\timesΩ$ at some later time. We prove the following rigidity result: If two Lorentzian metrics are close enough in some norm and if corresponding null-geodesics have equal lengths then the metrics are equal. |
| title | Rigidity for Lorentzian metrics with the same length of null-geodesics |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2205.05860 |