论文标题
Minkowski空间的全球外部稳定性：Einstein-Yang-Mills耦合
Global exterior stability of the Minkowski space: coupled Einstein-Yang-Mills perturbations
论文作者
论文摘要
在这里，我们证明了在阳米尔斯源存在下的$ 3+1 $尺寸Minkowski时空的扰动的全球量规辐射估计。特别是，我们获得了一个新颖的量规估计，该估算是在一组紧凑的Cauchy Slice集合的因果补体中，在双重零框架中与重力结合的Yang-Mills字段。结果的结果是在Yang-Mills扰动耦合下，Minkowski空间的全球外部稳定性。零比安奇方程和null Yang-mills方程中存在的特殊结构都至关重要地获得结论全球存在性质所需的分散估计值。直接使用Bel-Robinson和Yang-Mills应力 - 能量张量来获得能量估计值，以避免通过利用显然对称对称的双曲线特性和Null Bianchi和Null Yand-Mills方程的零件来支持加权整合。我们的结果适用于任何紧凑的半简单量规组。这是Minkowski空间的第一个稳定性结果，包括非线性源。
Here we prove a global gauge-invariant radiation estimates for the perturbations of the $3+1$ dimensional Minkowski spacetime in the presence of Yang-Mills sources. In particular, we obtain a novel gauge invariant estimate for the Yang-Mills fields coupled to gravity in a double null framework in the Causal complement of a compact set of a Cauchy slice. A consequence of our result is the global exterior stability of the Minkowski space under coupled Yang-Mills perturbations. A special structure present both in the null Bianchi equations and the null Yang-Mills equations is utilized crucially to obtain the dispersive estimates necessary to conclude the global existence property. Direct use of Bel-Robinson and Yang-Mills stress-energy tensor to obtain the energy estimates is avoided in favor of weighted integration by parts taking advantage of the manifestly symmetric hyperbolic characteristics of null Bianchi and null Yang-Mills equations. Our result holds for any compact semi-simple gauge group. This is the first stability result of Minkowski space including a non-linear source.
