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arXiv · 2503.19403

Extension principles for the Einstein Yang--Mills system

Junbin Li·Jinhua Wang
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Abstract

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.

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Junbin Li, Jinhua Wang. 2025-03-25. Extension principles for the Einstein Yang--Mills system. https://arxiv.org/abs/2503.19403

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