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Global exterior Cauchy problem for \(\text{spin }3/2\) zero rest-mass fields in the Schwarzschild space-time. (English) Zbl 0878.35115

The author sets out to study spin 3/2 fields from the point of view of hyperbolic partial differential equations. The purpose of the paper is to set up a technical basis which will allow further analytic investigations in the future. He chooses a particular Ricci-flat space-time, the Schwarzschild black hole, on which he solves the global Cauchy problem for the Dirac equation, \[ \nabla^{AA'} \sigma^C_{A'B'} =0, \] for the first potential of a spin 3/2 zero rest-mass field, for solutions with minimum regularity. This study is a first step towards the understanding of more difficult questions like the development of a time-dependent scattering theory for spin 3/2 fields on black hole space-times.

MSC:

35Q75 PDEs in connection with relativity and gravitational theory
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C57 Black holes
83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
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