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

We use a gauge fixing for the Rarita-Schwinger equations for helicity 3/2 fields in curved space that leads to a straightforward Hilbert space framework for their study and prove global existence and uniqueness of solutions to the Rarita-Schwinger evolution equations compatible with the constraints inthis framework. We discuss how these results might be applied to the global analysis of the full Einstein vacuum equations and provide a complete analysis as a basis for such applications. These and a programme for develop ing an scattering/inverse scattering transform for the full Einstein equations are discussed.