Mathematical Problems in General Relativity

研究引力的真空爱因斯坦方程时，不应对初始数据的大小施加任何对称性或限制。由一个被困区域产生的时空奇点的结构将被探索。应寻求导致演化形成圈闭区域的初始条件。应研究非由被困区域形成奇点的可能性。应寻求解决方案局部可扩展性的准则，以改进已知结果。此外，还应努力建立克尔解的变分表征。用两相流体模型表示物质的球对称爱因斯坦方程的研究工作应继续下去，目的是描述导致黑洞或中子星形成这两种选择的初始条件。最后，在狭义相对论的框架下研究不受球对称限制的两相模型。这些数学研究将提供对引力理论中困难的基本问题的见解

***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.***