Extension principles for the Einstein Yang--Mills system

2025/03/25 by Li, Junbin, Wang, Jinhua
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.2503.19403

Abstract

We prove the local existence theorem and establish an extension principle for the spherically symmetric Einstein Yang--Mills system (SSEYM) with H¹ 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^∞-L^∞ estimate, fails in the Yang--Mills context. Instead, we employ an L²-based method, which is valid for both massless and massive scalar matter fields as well.

Related

• Stable regular solution of Einstein-Yang-Mills equation
• A new symmetric hyperbolic formulation and the local Cauchy problem for the Einstein--Yang--Mills system in the temporal gauge
• Formation of trapped surfaces in the Einstein-Yang-Mills system
• Local well-posedness of the Einstein-Yang-Mills system in CMCSHGC gauge
• A Numerical Exploration of the Spherically Symmetric SU(2) Einstein-Yang-Mills Equations