RUI: Studies of Singularities

RUI：奇点研究

• 批准号: 9408439
• 负责人: David Garfinkle
• 金额: $ 4.35万
• 依托单位: Oakland University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9408439&HistoricalAwards=false
• 关键词: RUI; Studies; Singularities

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.

奇点定理告诉我们，奇点形成于一大类时空中，包括大爆炸和星星引力坍缩形成黑洞的物理相关情形。 然而，这些定理很少告诉我们关于奇点的性质。 例如，我们想知道不完全观测者的整个类别，曲率如何沿着他们的世界线表现，以及他们是否能在撞到奇点之前看到奇点。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于研究奇点的方法：（i）找到精确解并研究其奇点;（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以解决这些问题。 轴对称宇宙学一般初始数据的数值演化将用于研究空间非均匀模型奇异性的方法。 他将研究广义相对论和弦论中的非奇异、定常电真空解。 他还将探讨Choptuik的缩放行为的数值发现，在形成一个零质量奇点从崩溃的球形标量场使用规范不变零初始值制定。 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后面的问题。 Shapiro和Teukolsky的工作表明，高度长扁的物体可以在引力坍缩过程中形成裸奇点。 作为一种替代方案，他将开始对高度扁长重力波的坍缩进行数值研究，以确定是否会形成裸奇点。