Book Review: Geometric relativity
Book Review: Geometric relativity
复制标题
书评：几何相对论
DOI：
10.1090/bull/1736
复制
发表时间：
2021
影响因子：
1.3
通讯作者：
Huang, Lan-Hsuan
中科院分区：
文献类型：
--
作者：
Huang, Lan-Hsuan
让我们开始简要的历史帐户如何广义相对论最终满足数学的分支称为几何分析。爱因斯坦的广义相对论在很大程度上建立在洛伦兹流形上，称为时空。尽管广义相对论有其几何框架，但它在很长一段时间内被视为物理学的一个分支。在爱因斯坦发表他的第一篇关于广义相对论的论文后的近半个世纪，1973年，美国数学学会在斯坦福大学举行了一次为期两周的微分几何会议，其中包括一次广义相对论的会议。在这次会议上，理论物理学家R。Geroch和数学家J. Kazdan和F.华纳分别从看似非常不同的动机发布问题。一个问题是关于能量/质量的正性的基本问题，这是物理界感兴趣的，而另一个问题则是出于对拓扑和正标量曲率度量之间联系的更广泛的知识好奇心。然而，这两个问题都得出了同样的猜想：
Let us begin with a brief historic account on how the theory of general relativity eventually met the branch of mathematics called geometric analysis. Einstein’s theory of general relativity is largely built upon a Lorentzian manifold, called spacetime. Despite its geometric framework, general relativity had been for a long time viewed as a branch of physics. Almost a half century later after Einstein published his first paper on general relativity, in 1973 a two-week American Mathematical Society conference on differential geometry held at Stanford University had included a session of general relativity. In this conference, the theoretical physicist R. Geroch and mathematicians J. Kazdan and F. Warner separately posted problems from seemingly very different motivations. One problem is a fundamental problem about positivity of energy/mass that is of interest to the physics community, while the other is motivated by a broader intellectual curiosity about connections between topology and metrics of positive scalar curvature. Nevertheless, both problems arrive at the same conjecture: