Characteristic Gluing with $Λ$: III. High-differentiability nonlinear gluing
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912850118705152 |
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| author | Chruściel, Piotr T. Cong, Wan Gray, Finnian |
| author_facet | Chruściel, Piotr T. Cong, Wan Gray, Finnian |
| contents | We prove a nonlinear characteristic $C^k$-gluing theorem for vacuum gravitational fields in Bondi gauge for a class of characteristic hypersurfaces near static vacuum $n$-dimensional backgrounds, $n\ge 3$, with any finite $k$, with cosmological constant $ Λ\in \mathbb{R}$, near Birmingham-Kottler backgrounds. This generalises the $C^2$-gluing of Aretakis, Czimek and Rodnianski, carried-out near light cones in four-dimensional Minkowski spacetime. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_03903 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characteristic Gluing with $Λ$: III. High-differentiability nonlinear gluing Chruściel, Piotr T. Cong, Wan Gray, Finnian General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs Differential Geometry We prove a nonlinear characteristic $C^k$-gluing theorem for vacuum gravitational fields in Bondi gauge for a class of characteristic hypersurfaces near static vacuum $n$-dimensional backgrounds, $n\ge 3$, with any finite $k$, with cosmological constant $ Λ\in \mathbb{R}$, near Birmingham-Kottler backgrounds. This generalises the $C^2$-gluing of Aretakis, Czimek and Rodnianski, carried-out near light cones in four-dimensional Minkowski spacetime. |
| title | Characteristic Gluing with $Λ$: III. High-differentiability nonlinear gluing |
| topic | General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2407.03903 |