标题： 开Milne时空的全局稳定性 显示英文标题

标题： Global stability of the open Milne spacetime

摘要： 开放的Milne宇宙时空有一个三维的柯西面，其等距于非紧致的双曲空间。 我们证明了对于有质量和无质量的爱因斯坦-标量场方程，开放的Milne时空具有全局非线性稳定性，并表明当时间趋于无穷时，空间度规趋向于双曲度规。 证明基于高斯规范坐标，在这些坐标中，引力的衰减率由Milne时空的膨胀几何决定。 显示英文摘要

摘要： The open Milne cosmological spacetime has a 3-dimensional Cauchy surface isometric to the (non-compact) hyperbolic space. We prove the globally nonlinear stability of the open Milne spacetime for both massive and massless Einstein-scalar field equations and show that as time goes to infinity, the spatial metric tends to the hyperbolic metric. The proof is based on the Gaussian normal coordinates, in which the decay rates of gravity are determined by the expanding geometry of Milne spacetime.