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GLOBAL RESULTS FOR THE RARITA–SCHWINGER EQUATIONS AND EINSTEIN VACUUM EQUATIONS

Published online by Cambridge University Press:  01 November 1999

L. J. MASON  and
J. P. NICOLAS
L. J. MASON
Affiliation:
The Mathematical Institute, 24–29 St Giles', Oxford OX1 3LB, email: lmason@maths.ox.ac.uk
J. P. NICOLAS
Affiliation:
Institut de Mathématiques M.A.B. Université Bordeaux 1 351 Cours de la Libération 33405 Talence cedex France, email: nicolas@math.u-bordeaux.fr
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Abstract

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.

1991 Mathematics Subject Classification: 83C60, 35Q75, 83C05, 35L45.

Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 79 , Issue 3 , November 1999 , pp. 694 - 720
Copyright
1999 London Mathematical Society

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