Ricci fall-off in static and stationary, globally hyperbolic, non-singular spacetimes
Ricci fall-off in static and stationary, globally hyperbolic, non-singular spacetimes
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静态和静止、全局双曲、非奇异时空中的里奇衰减
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
S. G. Harris
中科院分区：
文献类型：
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作者：
D. Garfinkle;S. G. Harris
如果一个时空的里奇曲率足以产生测地线的收敛（例如奇点定理的前提条件），但却不存在奇点，那么这个时空有什么限制呢？我们回答这个问题的一个限制类的时空：静态或静止，测地线完成，和全球双曲。答案是，在至少一个类空方向上，在静止观测者空间上自然出现的黎曼度量中，里奇曲率必须以逆二次的速率衰减（广义地说）。沿着的方式，我们建立了一些全球性的结果，在固定的观察者空间，关于其完整性和它的行为方面的普遍覆盖空间，我们还定义了一个新的几何不变的固定时空，相关的因果行为（除其他事项外）。
What restrictions are there on a spacetime for which the Ricci curvature is such as to produce convergence of geodesics (such as the preconditions for the singularity theorems) but for which there are no singularities? We answer this question for a restricted class of spacetimes: static or stationary, geodesically complete, and globally hyperbolic. The answer is that, in at least one spacelike direction, the Ricci curvature must fall off (in a generalized manner of speaking) at a rate inversely quadratic in a naturally-occurring Riemannian metric on the space of stationary observers. Along the way, we establish some global results on the stationary observer space, regarding its completeness and its behaviour with respect to universal covering spaces; we also define a new geometric invariant for stationary spacetimes, related to causal behaviour (among other things).