Formation of trapped surfaces for the Einstein--Maxwell--charged scalar field system
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910920851062784 |
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| author | Shen, Dawei Wan, Jingbo |
| author_facet | Shen, Dawei Wan, Jingbo |
| contents | In this paper, we prove a scale-critical trapped surface formation result for the Einstein--Maxwell--charged scalar field (EMCSF) system, without any symmetry assumptions. Specifically, we establish a scale-critical semi-global existence theorem from past null infinity and show that the focusing of gravitational waves, the concentration of electromagnetic fields, or the condensation of complex scalar fields, each individually, can lead to the formation of a trapped surface. In addition, we capture a nontrivial charging process along past null infinity, which introduces new difficulties due to the abnormal behavior of the matter fields. Nevertheless, the semi-global existence result and the formation of a trapped surface remain valid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19976 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Formation of trapped surfaces for the Einstein--Maxwell--charged scalar field system Shen, Dawei Wan, Jingbo Analysis of PDEs General Relativity and Quantum Cosmology Differential Geometry In this paper, we prove a scale-critical trapped surface formation result for the Einstein--Maxwell--charged scalar field (EMCSF) system, without any symmetry assumptions. Specifically, we establish a scale-critical semi-global existence theorem from past null infinity and show that the focusing of gravitational waves, the concentration of electromagnetic fields, or the condensation of complex scalar fields, each individually, can lead to the formation of a trapped surface. In addition, we capture a nontrivial charging process along past null infinity, which introduces new difficulties due to the abnormal behavior of the matter fields. Nevertheless, the semi-global existence result and the formation of a trapped surface remain valid. |
| title | Formation of trapped surfaces for the Einstein--Maxwell--charged scalar field system |
| topic | Analysis of PDEs General Relativity and Quantum Cosmology Differential Geometry |
| url | https://arxiv.org/abs/2504.19976 |