Static- and stationary-complete spacetimes: algebraic and causal structures
Static- and stationary-complete spacetimes: algebraic and causal structures
复制标题
静态和静态完全时空：代数和因果结构
DOI：
--
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
S. G. Harris
中科院分区：
文献类型：
--
作者：
S. G. Harris
本文旨在分析具有完全(类时)杀伤场的静态和静态时空的整体性质，并特别注意群作用的商。这是用代数结构表示的，这种结构对于静态情况相当简单，而对于静态情况则更复杂；最重要的工具，基本余循环，是静态时空的上同调类，但在静态情况下具有更松散的结构。具体来说：(1)设计了一种类似于Minkowski空间中的时空间隔的新的度量方法，用于检测静止时空中的两点是否具有因果关系；这被证明是非常有用的分析方法。(2)所有静止的时空都是通过它们相对于基本共周期的行为来分类的；这使得能够完整地刻画全局因果关系性质。(3)说明了这些工具是如何确定一个静止时空的整体双曲性是否由它的商继承的。(4)详细地考察了大量的例子，包括数学上的好奇心和物理上感兴趣的例子，例如平坦的、加速的、Schwarzschild的、Kerr的和其他背景中的宇宙弦。
This is intended as an analysis of the global properties of static and stationary spacetimes with complete (timelike) Killing field, with particular attention to quotients by group actions. This is presented in terms of algebraic structures which are fairly simple for the static case and more involved for the stationary case; the most important tool, the fundamental cocycle, is a cohomological class for static spacetimes but of somewhat looser structure in the stationary case. In particular: (1) A new measurement, similar to the spacetime interval in Minkowski space, is devised for detecting whether two points are causally related in a stationary spacetime; this proves very useful for analysis. (2) All stationary spacetimes are categorized by how they behave with respect to the fundamental cocycle; this enables a complete characterization of global causality properties. (3) It is shown how these tools determine whether global hyperbolicity of a stationary spacetime is inherited by its quotients. (4) Examples are examined in detail, a large range including both ones of mathematical curiosity and ones of physical interest, such as cosmic strings in flat, accelerated, Schwarzschild, Kerr, and other backgrounds.