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Cosmic Censorship for Gowdy Spacetimes

机译:高迪时空的宇宙审查

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摘要

Due to the complexity of Einstein’s equations, it is often natural to study a question of interest in the framework of a restricted class of solutions. One way to impose a restriction is to consider solutions satisfying a given symmetry condition. There are many possible choices, but the present article is concerned with one particular choice, which we shall refer to as Gowdy symmetry. We begin by explaining the origin and meaning of this symmetry type, which has been used as a simplifying assumption in various contexts, some of which we shall mention. Nevertheless, the subject of interest here is strong cosmic censorship. Consequently, after having described what the Gowdy class of spacetimes is, we describe, as seen from the perspective of a mathematician, what is meant by strong cosmic censorship. The existing results on cosmic censorship are based on a detailed analysis of the asymptotic behavior of solutions. This analysis is in part motivated by conjectures, such as the BKL conjecture, which we shall therefore briefly describe. However, the emphasis of the article is on the mathematical analysis of the asymptotics, due to its central importance in the proof and in the hope that it might be of relevance more generally. The article ends with a description of the results that have been obtained concerning strong cosmic censorship in the class of Gowdy spacetimes.
机译:由于爱因斯坦方程式的复杂性,在有限类解的框架内研究感兴趣的问题通常很自然。施加限制的一种方法是考虑满足给定对称条件的解。有许多可能的选择,但是本文涉及一种特定的选择,我们将其称为高迪对称。我们首先解释这种对称类型的起源和含义,该对称类型已在各种情况下用作简化假设,我们将在其中提及其中一些。尽管如此,这里感兴趣的主题是强大的宇宙审查。因此,在描述了时空的Gowdy类之后,我们从数学家的角度描述了什么是强宇宙审查。关于宇宙检查的现有结果是基于对解的渐近行为的详细分析。这种分析部分是由诸如BKL猜想之类的猜想所激发的,因此我们将对其进行简要描述。但是,由于其在证明中的重要作用,并希望它可能在更一般的意义上具有重要意义,因此本文的重点是对渐近性进行数学分析。本文最后描述了在Gowdy时空类中有关强宇宙审查的结果。

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