奇点与时空边界的概率观
Probabilistic view on singularities and spacetime boundary
摘要：
本文的目的是促进概率方法在数学广义相对论问题研究中的应用。用概率方法证明了两个新的、简单的奇异性定理，它们的特点不同于经典的奇异性定理。在某些能量条件下，没有任何因果或初始/边界假设，能量流的简单条件意味着概率不完备性。此外，我们引入了一个概率的时空边界的概念，它没有经典边界可能具有的病理缺陷。
英文摘要：
The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity theorems, are proved using probabilistic methods. Under some energy conditions, and without any causal or initial/boundary assumption, simple conditions on the energy flow imply probabilistic incompleteness. Also we introduce a probabilistic notion of spacetime boundary which has none of the pathological defects that the classical boundaries may have.
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