Mathematical Problems in General Relativity

* 9800115Christodoulou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。 将探索由陷获区域产生的时空奇点的结构。 应寻求导致形成俘获区的初始条件。 应研究不是由俘获区引起的奇点形成的可能性。 应寻求解的局部可拓性准则，以改进已知结果。 此外，应努力建立克尔解的变分表征。 将继续进行以两相流体模型表示物质的球对称爱因斯坦方程的工作，目的是确定导致黑洞或中子星星形成这两种选择的初始条件。 最后，我们将在狭义相对论的框架内研究不受球对称性限制的两相模型，这些数学研究将有助于深入了解引力理论中的一些困难的基本问题。*

***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.***