Extension principles for the Einstein Yang--Mills system
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911131041267712 |
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| author | Li, Junbin Wang, Jinhua |
| author_facet | Li, Junbin Wang, Jinhua |
| contents | We prove the local existence theorem and establish an extension principle for the spherically symmetric Einstein Yang--Mills system (SSEYM) with $H^1$ data. This in addition implies Cauchy stability for the system.
In contrast to a massless scalar field, the purely magnetic Yang--Mills field in spherical symmetry satisfies a wave-type equation with a singular potential. As a consequence, the proof of Christodoulou [10], based on an $L^\infty-L^\infty$ estimate, fails in the Yang--Mills context. Instead, we employ an $L^2$-based method, which is valid for both massless and massive scalar matter fields as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19403 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extension principles for the Einstein Yang--Mills system Li, Junbin Wang, Jinhua General Relativity and Quantum Cosmology Analysis of PDEs Differential Geometry We prove the local existence theorem and establish an extension principle for the spherically symmetric Einstein Yang--Mills system (SSEYM) with $H^1$ data. This in addition implies Cauchy stability for the system. In contrast to a massless scalar field, the purely magnetic Yang--Mills field in spherical symmetry satisfies a wave-type equation with a singular potential. As a consequence, the proof of Christodoulou [10], based on an $L^\infty-L^\infty$ estimate, fails in the Yang--Mills context. Instead, we employ an $L^2$-based method, which is valid for both massless and massive scalar matter fields as well. |
| title | Extension principles for the Einstein Yang--Mills system |
| topic | General Relativity and Quantum Cosmology Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2503.19403 |