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.
