论文标题
爱因斯坦 - 克莱因·戈登（Einstein-Klein-gordon）的空间
Einstein-Klein-Gordon spacetimes in the harmonic near-Minkowski regime
论文作者
论文摘要
We study the initial value problem for the Einstein-Klein-Gordon system and establish the global nonlinear stability of massive matter in the near-Minkowski regime when the initial geometry is a perturbation of an asymptotically flat, spacelike hypersurface in Minkowski spacetime and the metric enjoys the harmonic decay 1/r (in term of a suitable distance function r at spatial infinity).我们的分析涵盖了具有较小能量规范的物质领域，并且仅在Spacelike Infinity处享有缓慢的衰减。我们的证明是基于作者最近引入的欧几里得 - 杂胶体叶状方法，并区分了沿渐近双曲线切片的衰变和沿渐近层状层状切片的衰变。我们仔细分析了谐波1/r的度量分量的衰减，尤其是在光锥方向上的度量分量。在存在这样慢旧的物质领域的情况下，我们为爱因斯坦方程式建立了一个全球存在理论，其表示为非线性波和klein-gordon方程的耦合系统。
We study the initial value problem for the Einstein-Klein-Gordon system and establish the global nonlinear stability of massive matter in the near-Minkowski regime when the initial geometry is a perturbation of an asymptotically flat, spacelike hypersurface in Minkowski spacetime and the metric enjoys the harmonic decay 1/r (in term of a suitable distance function r at spatial infinity). Our analysis encompasses matter fields that have small energy norm and solely enjoys a slow decay at spacelike infinity. Our proof is based on the Euclidean-hyperboloidal foliation method recently introduced by the authors, and distinguishes between the decay along asymptotically hyperbolic slices and the decay along asymptotically Euclidean slices. We carefully analyze the decay of metric component at the harmonic level 1/r, especially the metric component in the direction of the light cone. In presence of such a slow-decaying matter field, we establish a global existence theory for the Einstein equations expressed as a coupled system of nonlinear wave and Klein-Gordon equations.
