Formation of Trapped Surfaces in Geodesic Foliation
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866913513044180992 |
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| author | Chen, Xuantao Klainerman, Sergiu |
| author_facet | Chen, Xuantao Klainerman, Sergiu |
| contents | We revisit the classical results of the formation of trapped surfaces for the Einstein vacuum equation relying on the geodesic foliation, rather than the double null foliation used in all previous results, starting with the seminal work of Christodoulou \cite{Chr1} and continued in \cite{KRodn}, \cite{An}, \cite{AnLuk}, \cite{KLR}, \cite{An1}. The main advantage of the method is that it only requires information on the incoming curvature along the incoming initial null hypersurface. The result is based on a version of the non-integrable PT frame introduced in \cite{KS:Kerr} and \cite{GKS}, associated to the geodesic foliation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14582 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Formation of Trapped Surfaces in Geodesic Foliation Chen, Xuantao Klainerman, Sergiu General Relativity and Quantum Cosmology Analysis of PDEs Differential Geometry We revisit the classical results of the formation of trapped surfaces for the Einstein vacuum equation relying on the geodesic foliation, rather than the double null foliation used in all previous results, starting with the seminal work of Christodoulou \cite{Chr1} and continued in \cite{KRodn}, \cite{An}, \cite{AnLuk}, \cite{KLR}, \cite{An1}. The main advantage of the method is that it only requires information on the incoming curvature along the incoming initial null hypersurface. The result is based on a version of the non-integrable PT frame introduced in \cite{KS:Kerr} and \cite{GKS}, associated to the geodesic foliation. |
| title | Formation of Trapped Surfaces in Geodesic Foliation |
| topic | General Relativity and Quantum Cosmology Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2409.14582 |