On the Topology of Vacuum Spacetimes
On the Topology of Vacuum Spacetimes
复制标题
论真空时空的拓扑
DOI：
10.1007/s00023-003-0133-9
复制
发表时间：
2002
期刊：
影响因子：
--
通讯作者：
D. Pollack
中科院分区：
文献类型：
--
作者：
J. Isenberg;R. Mazzeo;D. Pollack
抽象的。我们证明了（n + 1）维真空爱因斯坦方程的渐近平坦解的空间拓扑不受限制。我们通过将任意紧致流形$ \Sigma^n $上的真空约束方程的解粘到$ \mathbb{R}^n $上的约束的渐近欧几里得解来实现这一点。对于任何不允许正标量曲率度量的$ \Sigma^n $，这提供了存在无极大切片的渐近平坦真空时空。我们的主要定理是一个特殊的情况下，一个更一般的胶合建设的非退化的真空约束方程的平均曲率有一些限制，但平均曲率不一定是常数的解决方案。这推广了构造[16]，其限于恒定平均曲率数据。
Abstract. We prove that there are no restrictions on the spatial topology of asymptotically flat solutions of the vacuum Einstein equations in (n + 1)-dimensions. We do this by gluing a solution of the vacuum constraint equations on an arbitrary compact manifold $ \Sigma^n $ to an asymptotically Euclidean solution of the constraints on $ \mathbb{R}^n $. For any $ \Sigma^n $ which does not admit a metric of positive scalar curvature, this provides for the existence of asymptotically flat vacuum spacetimes with no maximal slices. Our main theorem is a special case of a more general gluing construction for nondegenerate solutions of the vacuum constraint equations which have some restrictions on the mean curvature, but for which the mean curvature is not necessarily constant. This generalizes the construction [16], which is restricted to constant mean curvature data.