Mathematical Problems in General Relativity

广义相对论中的数学问题

• 批准号: 9800115
• 负责人: Demetrios Christodoulou
• 金额: $ 24.02万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-01 至 2002-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9800115&HistoricalAwards=false
• 关键词: Mathematical; Problems; General; Relativity

***9800115ChristodoulouThe vacuum Einstein equations for gravitation shall be studied without imposing any symmetry or restriction on the size of the initial data. The structure of spacetime singularities resulting from a trapped region shall be explored. Initial conditions which leads in evolution to the formation of trapped regions shall be sought. The possibility of singularity formation not resulting from a trapped region shall be investigated. Criteria for the local extendibility of solutions shall be sought to which improve known results. Also, an effort shall be made to establish a variational characterization of the Kerr solution. The work on the spherically symmetric Einstein equations with matter represented by the two-phase fluid model shall be continued with the aim of characterizing the initial conditions leading to the two alternatives: black hole or neutron star formation. Finally, the two-phase model without the restriction to spherical symmetry shall be studied in the framework of special relativity.These mathematical studies will provide insight into difficult fundamental questions in gravitation theory.***

*9800115克里斯托尔真空爱因斯坦引力方程的研究不应对初始数据的大小施加任何对称性或限制。应探索由陷阱区域产生的时空奇点的结构。应寻找导致形成圈闭区域的演化的初始条件。应调查不是由陷阱区域引起的奇点形成的可能性。应寻求解决方案局部可扩性的标准，以改进已知结果。此外，还应努力建立克尔解决方案的变分表征。用两相流体模型表示物质的球对称爱因斯坦方程的工作将继续进行，目的是描述导致两种选择的初始条件：黑洞或中子星的形成。最后，不受球对称限制的两相模型将在狭义相对论的框架内进行研究。这些数学研究将提供对引力理论中困难的基本问题的洞察。