全球时空相似性
Global Spacetime Similarity
摘要：
在固定流形上的洛伦兹度规空间中，有两类拓扑最常被放置。正如我对R. Geroch [Relativity，259（1970）; Gen. Rel.重力，2，61（1971）]，然而，这些标准类都没有正确地捕捉到全局时空相似性的概念。特别是，Geroch提出的例子来说明，一个，紧凑的开放拓扑，一般似乎太粗糙，而另一个，开放（惠特尼）拓扑，一般似乎太精细。在进一步阐述了这些失败的数学和物理原因之后，我构建了一个拓扑结构，成功地捕捉了全局时空相似性的概念，并研究了它的一些数学和物理性质。
英文摘要：
There are two classes of topologies most often placed on the space of Lorentz metrics on a fixed manifold. As I interpret a complaint of R. Geroch [Relativity, 259 (1970); Gen. Rel. Grav., 2, 61 (1971)], however, neither of these standard classes correctly captures a notion of global spacetime similarity. In particular, Geroch presents examples to illustrate that one, the compact-open topologies, in general seems to be too coarse, while another, the open (Whitney) topologies, in general seems to be too fine. After elaborating further the mathematical and physical reasons for these failures, I then construct a topology that succeeds in capturing a notion of global spacetime similarity and investigate some of its mathematical and physical properties.
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