论文标题
关于爱因斯坦 - 杨米尔斯系统的全球良好性
On the Global Well-Posedness of the Einstein-Yang-Mills System
论文作者
论文摘要
在本文中，我们在恒定平均平均外部曲率空间谐波和广义的库仑仪表中，对爱因斯坦 - 杨米尔斯系统的库奇问题的全球良好性和广义性库仑仪的全球性结果进行了部分结果。我们为一个$ n+1 $ dimiminations的家族提供了一个小型全球定理，并利用[Andersson and Moncrief，arxiv：0908.0784]中提出的能源论点。我们观察到，由于$ 3+1 $ yang-mills方程的形式不变性，这些能源论点将失败，并在$ 3+1 $尺寸中呈现量规范的量规格，以表明能量参数无法证明全球范围的良好型量子，而无需使用量子的范围。
In this paper, we present a partial result on the global well-posedness of the Cauchy problem for the Einstein-Yang-Mills system in the constant mean extrinsic curvature spatial harmonic and generalized Coulomb gauges as introduced in [Mondal, arXiv:2112.14273]. We give a small-data global existence theorem for a family of $n+1$ dimensional spacetimes with $n\geq4$, utilizing energy arguments presented in [Andersson and Moncrief, arXiv:0908.0784]. We observe that these energy arguments will fail for $n=3$ due to the conformal invariance of the $3+1$ Yang-Mills equations and present a gauge-covaraiant formulation of the Einstein-Yang-Mills system in $3+1$ dimensions to show that an energy argument cannot be used to prove the global well-posedness result, regardless of the choice of gauge.
