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The Problem of Evolution in General Relativity

广义相对论中的进化问题

基本信息

批准号：
0245368
负责人：
Sergiu Klainerman
金额：
$ 37.5万
依托单位：
Princeton University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2003
资助国家：
美国
起止时间：
2003-07-01 至 2007-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0245368&HistoricalAwards=false
关键词：
Problem Evolution General Relativity

项目摘要

PI: Sergiu Klainerman, Princeton UniversityDMS-0245368Abstract:The main goal of the proposal is to investigate the regularity properties of the Einstein field equations of General Relativity as well as those of other important physical systems. Most emphasis be given to the `` Bounded square integrable curvature conjecture'' according to which the initial value problem for the Einstein-vacuum equations is well posed with only square integrable bounds on the curvature of its initial data set. The PI believes that this is an essential foundational step towards a generalregularity theory of the Einstein equations. By concentrating on the issue of minimal regularity assumptions for which the equations can be uniquely continued it is hoped that we can find, at least, some of the tools needed in understanding the onset of singular behavior.One of the fundamental tasks of mathematical physics is to provide a full, qualitative, description of black holes and singularities of solutions to the Einstein equations in General Relativity. The principal investigator has established a programwhich he hopes that will provide the rigorous mathematical foundations of such a theory. The main goal of this present proposal is to establish the minimal regularity assumptions that needs to be verified by the initial conditions such that one can still make sense of a physical solution to the Einstein field equations. The proposal also envisages research in connection to other important equations of mathematical physics such as those governing the behavior of collisionless particles in an electromagnetic field.

主要研究者：Sergiu Klainerman，Princeton UniversityDMS-0245368摘要：该提案的主要目标是研究广义相对论爱因斯坦场方程以及其他重要物理系统的正则性。最重要的是给予“有界平方可积曲率”，根据它的爱因斯坦真空方程的初值问题是很好的设置只有平方可积的边界上的曲率的初始数据集。PI认为这是迈向爱因斯坦方程的一般规律性理论的重要基础步骤。通过集中讨论方程可以唯一连续的最小正则性假设问题，希望我们至少可以找到一些数学物理学的基本任务之一是对广义相对论中的爱因斯坦方程的解的黑洞和奇点提供一个完整的、定性的描述。首席研究员已经建立了一个程序，他希望这将提供严格的数学基础，这样一个理论。本提案的主要目标是建立需要由初始条件验证的最小正则性假设，以便人们仍然可以理解爱因斯坦场方程的物理解。该提案还设想研究与数学物理学的其他重要方程有关的问题，例如控制电磁场中无碰撞粒子行为的方程。