论文标题
全球时空相似性
Global Spacetime Similarity
论文作者
论文摘要
在固定的歧管上，最常将两类拓扑放在洛伦兹指标的空间上。当我解释R. Geroch的抱怨[相对论，259（1970）； Gen. Rel。但是，坟墓，第2卷，第61页（1971）]，但是，这些标准类都没有正确捕获全球时空相似性的概念。特别是，Geroch提出了示例，以说明一个示例，通常，紧凑型拓扑似乎太粗糙了，而另一个则是开放的（惠特尼）拓扑，总的来说似乎太好了。在进一步阐述了这些失败的数学和物理原因之后，我构建了一种拓扑结构，该拓扑成功地捕获了全球时空相似性的概念，并研究了其一些数学和物理特性。
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.
