The domain of dependence
The domain of dependence
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依赖域
DOI：
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发表时间：
1970
期刊：
影响因子：
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通讯作者：
R. Geroch
中科院分区：
文献类型：
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作者：
R. Geroch
本文综述了在引力场研究中特别有用的依赖域（柯西展开）的各种性质。构造证明和反例的基本技术进行了说明。介绍了一种新的处理时空整体性质的工具--过去和未来体积函数。这些函数被用来建立两个新的定理：（1）时空有柯西曲面的充分必要条件是它是全局双曲的;（2）柯西曲面的存在是时空的稳定性质。
The various properties of the domain of dependence (Cauchy development) which have been found particularly useful in the study of gravitational fields are reviewed. The basic techniques for constructing proofs and counterexamples are described. A new tool—the past and future volume functions—for treating certain global properties of space‐times is introduced. These functions are used to establish two new theorems: (1) a necessary and sufficient condition that a space‐time have a Cauchy surface is that it be globally hyperbolic; and (2) the existence of a Cauchy surface is a stable property of space‐times.