High-frequency backreaction for the Einstein equations under $\mathbb U(1)$ symmetry: from Einstein-dust to Einstein-Vlasov
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909661743022080 |
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| author | Huneau, Cécile Luk, Jonathan |
| author_facet | Huneau, Cécile Luk, Jonathan |
| contents | Given suitable small, localized, $\mathbb U(1)$-symmetric solutions to the Einstein-massless Vlasov system in an elliptic gauge, we prove that they can be approximated by high-frequency vacuum spacetimes. This extends previous constructions where the limiting spacetime solves the Einstein-(multiple) null dust system (i.e., where the limiting massless Vlasov field can be written as a finite sum of delta measures). The proof proceeds by first approximating solutions to the Einstein-massless Vlasov system by solutions to the Einstein-(multiple) null dust system, then approximating solutions to the Einstein-null dust system by vacuum solutions. In the process, we take the number of families of dusts to infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21779 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-frequency backreaction for the Einstein equations under $\mathbb U(1)$ symmetry: from Einstein-dust to Einstein-Vlasov Huneau, Cécile Luk, Jonathan General Relativity and Quantum Cosmology Analysis of PDEs Given suitable small, localized, $\mathbb U(1)$-symmetric solutions to the Einstein-massless Vlasov system in an elliptic gauge, we prove that they can be approximated by high-frequency vacuum spacetimes. This extends previous constructions where the limiting spacetime solves the Einstein-(multiple) null dust system (i.e., where the limiting massless Vlasov field can be written as a finite sum of delta measures). The proof proceeds by first approximating solutions to the Einstein-massless Vlasov system by solutions to the Einstein-(multiple) null dust system, then approximating solutions to the Einstein-null dust system by vacuum solutions. In the process, we take the number of families of dusts to infinity. |
| title | High-frequency backreaction for the Einstein equations under $\mathbb U(1)$ symmetry: from Einstein-dust to Einstein-Vlasov |
| topic | General Relativity and Quantum Cosmology Analysis of PDEs |
| url | https://arxiv.org/abs/2506.21779 |