Prof. Christodoulou will pursue rigorous mathematical studies of interest to gravitational research. A new proof of the global nonlinear stability of the vacuum (Minkowski space) will be given which avoids the use of maximal hypersurfaces. The concepts of local mass and angular momentum in general relativity will be investigated. The structure of singularities in spherically symmetric gravitational collapse will be analyzed. This should lead to understanding the good behavior of solutions of the spherically symmetric Einstein equations in the past of the apparent horizon. The proof of a theorem describing the formation of black holes and singularities for the general Einstein equations will be attempted.
