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Global results for the Rarita-Schwinger equations and Einstein vacuum equations. (English) Zbl 1065.83046

Summary: We prove global existence and uniqueness of solutions to the Rarita-Schwinger evolution equations compatible with the constraints. 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. We explain 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 developing a scattering/inverse scattering transform for the full Einstein equations are discussed.

MSC:

83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
35Q75 PDEs in connection with relativity and gravitational theory
53C80 Applications of global differential geometry to the sciences
58J45 Hyperbolic equations on manifolds
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
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