Evolution problem in General Relativity

广义相对论中的演化问题建议研究摘要Sergiu Klainerman研究的重点是爱因斯坦场方程解的演化的数学分析。注意力将集中在这些解决方案的一些说明。一个是曲率张量与时空因果几何之间的关系。两个关注的现象“宇宙审查”，其他关注的渐近行为或“最终状态”和一个关于稳定的克尔解决方案。这些问题的解决需要研究洛伦兹流形的几何和曲率之间的关系以及爱因斯坦方程的分析。爱因斯坦的方程是广义相对论的场方程，它们的分析是理解宇宙学中许多问题的核心，包括黑洞和引力波理论。这些方程只有几个已知的精确解，本研究将进行更多的数学分析，以证明有关解决方案的定性结果。这种分析也应该有助于这些方程的数值计算的解决方案的算法的发展。

Evolution Problem in General Relativity Abstract of Proposed ResearchSergiu KlainermanThe research focuses on the mathematical analysis of the evolution of the solutions of the Einstein-field equations. Attention will be concentrated on a number of conjectures about these solutions. One concerns the relationship between the curvature tensor and the causal geometry of space-time. Two concern the phenomenon of "cosmic censorship", other concerns the asymptotic behavior or "final state" and one about the stability of the Kerr solution. The resolution of these problems will require the study of the relationship between geometry and curvature of Lorentzian manifolds as well as analysis of the Einstein equations. Einstein's equations are the field equations of general relativity and their analysis is central to the understanding of many issues in cosmology including the theory of black holes and gravitational waves. There are only a few exact solutions known of these equations and this research will pursue a more mathematical analysis that will prove qualitative results about the solutions. This analysis should also help the development of algorithms for the numerical computation of solutions of these equations.