U.S.-France Cooperative Research: Global Studies of Einstein Spacetimes

该奖项将支持数学领域的合作 耶鲁大学的Vincent Moncrief博士和 法国巴黎第六大学Yvonne Choquet-Bruhat博士。 该项目的主要目标是取得新的成果 关于宇宙学的大类的整体行为 爱因斯坦方程的解 研究人员的目的是表征最大柯西 这种时空的发展，通过提供类似的 广义相对论的整体存在性定理 他们 也将研究奇异解的边界行为 并希望得到扩展方法， 把一个显微镜放在时空奇点上 并将其归类为几何自然 路上了 这些目标一直是长期的挑战， 广义相对论，但现在的数学方法是 这可能会使真正的进展， 根本问题。 早期的全局存在结果 具有高对称性的时空现在可以扩展到非常 更大的解决方案和新技术系列，例如 作为“多尺度”方法的应用， 提供必要的工具， 时空奇点 这个基本方法 研究将试图扩大适用范围 建立数学方法，如使用 光锥和高阶能量估计，以更大， 不太对称的时空家族，同时 时间，开发新的方法，如扩展 上面提到的技术。这项研究将有利于 从美国和法国投资的广泛专业知识， 数学广义相对论领域的专家。

This award will support collaboration in mathematical physics between Dr. Vincent Moncrief, Yale University and Dr. Yvonne Choquet-Bruhat, University of Paris VI, France. The main objective of the project is to obtain new results on the global behavior of large classes of cosmological solutions of Einstein's equations. The investigators aim to characterize the maximal Cauchy developments of such spacetimes by providing the analogue of global existence theorems for general relativity. They will also study the boundary behavior of singular solutions and hope to derive expansion methods which will allow one to "put a microscope" on the spacetime singularities themselves and to classify them in a geometrically natural way. These aims have been longstanding challenges to general relativists, but now mathematical methods are becoming available which may allow genuine progress on such fundamental problems. Earlier global existence results for spacetimes with high symmetry may now be extendible to very much larger families of solutions and new techniques, such as the application of the method of "multiple scales", may provide the needed tools for the analytical study of spacetime singularities. The basic approach of this research will be to try to extend the range of applicability of the established mathematical methods, such as the use of light-cone and higher order energy estimates, to larger and less symmetric families of spacetimes, and at the same time, to develop new methods, such as the expansion techniques alluded to above. This research will benefit from the extensive expertise of the US and French investi- gators in the area of mathematical general relativity.