Class A spacetimes
Class A spacetimes
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DOI：
10.1007/s10711-011-9671-3
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发表时间：
2010-12
影响因子：
0.5
通讯作者：
S. Suhr
中科院分区：
文献类型：
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作者：
S. Suhr
我们引入A类时空，即紧致恶性时空（M,g），使得阿贝尔覆盖是全局双曲的。我们使用类似于Sullivan （Invent Math 36:25 - 255, 1976）和Burago （Adv Sov Math 9:20 0 - 210, 1992）所介绍的方法来研究A类时空的主要性质。因此，我们能够将允许a类度量的流形完全描述为映射环面。进一步，我们证明了A类时空的概念等同于加洛韦（Comm Math Phys 96:423-429, 1984）中引入的SCTP（空间紧致时间周期）时空的概念。在洛伦兹度量集合上的0拓扑中，证明了A类时空集合是开的。作为一个应用，我们证明了阿贝尔覆盖的时间分离的粗糙Lipschitz性质。这个粗糙的利普希茨性质是洛伦兹几何中奥布里-马瑟理论研究的一个重要部分。
We introduce class A spacetimes, i.e. compact vicious spacetimes (M,g) such that the Abelian coveris globally hyperbolic. We study the main properties of class A spacetimes using methods similar to those introduced in Sullivan (Invent Math 36:225–255, 1976) and Burago (Adv Sov Math 9:205–210, 1992). As a consequence we are able to characterize manifolds admitting class A metrics completely as mapping tori. Further we show that the notion of class A spacetime is equivalent to that of SCTP (spacially compact time-periodic) spacetimes as introduced in Galloway (Comm Math Phys 96:423–429, 1984). The set of class A spacetimes is shown to be open in theC0-topology on the set of Lorentzian metrics. As an application we prove a coarse Lipschitz property for the time separation of the Abelian cover. This coarse Lipschitz property is an essential part in the study of Aubry-Mather theory in Lorentzian geometry.