Global Results for the Rarita-Schwinger Equations and Einstein Vacuum Equations

We prove global existence and uniqueness of solutions to theRarita-Schwinger evolution equations compatible with the constraints.We use a gauge fixing for the Rarita-Schwinger equations forhelicity 3/2 fields in curved space that leads to a straightforwardHilbert space framework for their study. We explain how theseresults might be applied to the global analysis of the fullEinstein vacuum equations and provide a complete analysis asa basis for such applications. These and a programme for developinga scattering/inverse scattering transform for the full Einsteinequations are discussed. 1991 Mathematics Subject Classification:83C60, 35Q75, 83C05, 35L45.