RUI: Studies of Singularities

奇点定理告诉我们，奇点形成在一大类时空中，包括大爆炸和恒星引力坍塌形成黑洞的物理相关情况。然而，这些定理很少告诉我们奇点的性质。例如，我们想知道整类不完整的观察者，曲率是如何沿着他们的世界线表现的，以及他们是否能在击中奇点之前看到它。由于我们没有爱因斯坦方程的封闭形式的通解，加芬克尔教授打算使用所有可用的方法来研究奇点：(I)找到精确解并研究它们的奇点；(Ii)证明关于奇异时空行为的定理；或(Iii)对具有奇点的时空进行数值研究来解决这些问题。轴对称宇宙的一般初始数据的数值演化将被用来研究空间非均匀模型的奇异性的方法。他将在广义相对论和弦理论中研究非奇异的、静止的电空泡解。他还将探索肖普图伊克在利用规范不变零初值公式从球标量场的坍塌中形成零质量奇点的标度行为的数值发现。也许奇点研究中最重要的问题是宇宙审查：奇点是否隐藏在事件视界之后的问题。夏皮罗和特科尔斯基的研究表明，高度拉长的物体可以在引力崩塌时形成裸露的奇点。作为另一种选择，他将开始对高度延长的引力波的坍塌进行数值研究，看看是否形成了裸露的奇点。

The singularity theorems tell us that singularities form in a large class of spacetimes, including the physically relevant cases of the big bang and of the gravitational collapse of a star to form a black hole. However, these theorems tell us very little about the nature of the singularities. For example, we would like to know the entire class of incomplete observers, how the curvature behaves along their world lines and whether they can see the singularity before they hit it. Since we do not have the general solution of Einstein's equation in closed form, Prof. Garfinkle intends to use all the methods available for the study of singularities: (i) to find exact solutions and study their singularities; (ii) to prove theorems about the behavior of singular spacetimes or (iii) to perform a numerical study of spacetimes with singularities to address these issues. Numerical evolution of generic initial data for axisymmetric cosmologies will be used to study the approach to the singularity of spatially inhomogeneous models. He will examine nonsingular, stationary electrovac solutions in general relativity and in string theory. He will also explore Choptuik's numerical discovery of scaling behavior in the formation of a zero mass singularity from the collapse of a spherically scalar field using a gauge invariant null initial value formulation. Perhaps the most important problem in the study of singularities is cosmic censorship: the issue of whether singularities are hidden behind event horizons. Work by Shapiro and Teukolsky suggests that highly prolate objects can form naked singularities during gravitational collapse. As an alternative, he will start a numerical investigation of the collapse of highly prolate gravity waves to see whether a naked singularity forms.