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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/2208.01842 |
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| _version_ | 1866915574926278656 |
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| author | Eskin, Gregory |
| author_facet | Eskin, Gregory |
| contents | We consider a Lorentzian metric in $\mathbb{R}\times\mathbb{R}^n$. We show that if we know the lengths of the space-time geodesics starting at $(0,y,η)$ when $t=0$, then we can recover the metric at $y$. We prove the rigidity of Lorentzian metrics. We also prove a variant of the rigidity property for the case of null-geodesics: if two metrics are close and if corresponding null-geodesics have equal Euclidian lengths then the metrics are equal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_01842 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Remarks on the determination of the Lorentzian metric by the lengths of geodesics or null-geodesics Eskin, Gregory Analysis of PDEs We consider a Lorentzian metric in $\mathbb{R}\times\mathbb{R}^n$. We show that if we know the lengths of the space-time geodesics starting at $(0,y,η)$ when $t=0$, then we can recover the metric at $y$. We prove the rigidity of Lorentzian metrics. We also prove a variant of the rigidity property for the case of null-geodesics: if two metrics are close and if corresponding null-geodesics have equal Euclidian lengths then the metrics are equal. |
| title | Remarks on the determination of the Lorentzian metric by the lengths of geodesics or null-geodesics |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2208.01842 |