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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | https://arxiv.org/abs/2402.17598 |
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| _version_ | 1866916276567277568 |
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| author | Floch, Bruno Le LeFloch, Philippe G. |
| author_facet | Floch, Bruno Le LeFloch, Philippe G. |
| contents | To construct asymptotically-Euclidean Einstein's initial data sets, we introduce the localized seed-to-solution method, which projects from approximate to exact solutions of the Einstein constraints. The method enables us to glue together initial data sets in multiple asymptotically-conical regions, and in particular construct data sets that exhibit the gravity shielding phenomenon, specifically that are localized in a cone and exactly Euclidean outside of it. We achieve optimal shielding in the sense that the metric and extrinsic curvature { are controlled at a super-harmonic rate, regardless of how slowly they decay (even} beyond the standard ADM formalism), and the gluing domain can be a collection of arbitrarily narrow nested cones. We also uncover several notions of independent interest: silhouette functions, localized ADM modulator, and relative energy-momentum vector. An axisymmetric example is provided numerically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17598 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal shielding for Einstein gravity Floch, Bruno Le LeFloch, Philippe G. General Relativity and Quantum Cosmology Analysis of PDEs To construct asymptotically-Euclidean Einstein's initial data sets, we introduce the localized seed-to-solution method, which projects from approximate to exact solutions of the Einstein constraints. The method enables us to glue together initial data sets in multiple asymptotically-conical regions, and in particular construct data sets that exhibit the gravity shielding phenomenon, specifically that are localized in a cone and exactly Euclidean outside of it. We achieve optimal shielding in the sense that the metric and extrinsic curvature { are controlled at a super-harmonic rate, regardless of how slowly they decay (even} beyond the standard ADM formalism), and the gluing domain can be a collection of arbitrarily narrow nested cones. We also uncover several notions of independent interest: silhouette functions, localized ADM modulator, and relative energy-momentum vector. An axisymmetric example is provided numerically. |
| title | Optimal shielding for Einstein gravity |
| topic | General Relativity and Quantum Cosmology Analysis of PDEs |
| url | https://arxiv.org/abs/2402.17598 |