Nicolas, Jean-Philippe Global exterior Cauchy problem for \(\text{spin }3/2\) zero rest-mass fields in the Schwarzschild space-time. (English) Zbl 0878.35115 Commun. Partial Differ. Equations 22, No. 3-4, 465-502 (1997). 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. Reviewer: A.D.Osborne (Keele) Cited in 7 Documents 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 Keywords:spin 3/2 fields; Schwarzschild black hole; global Cauchy problem; Dirac equation PDF BibTeX XML Cite \textit{J.-P. Nicolas}, Commun. Partial Differ. Equations 22, No. 3--4, 465--502 (1997; Zbl 0878.35115) Full Text: DOI OpenURL References: [1] Bachelot A., Ann. Inst. Henri Poincaré 54 pp 261– (1991) [2] DOI: 10.1007/BF02859608 · Zbl 0082.22005 [3] Chandrasekhar S., Oxford Science Publications Publications, Oxford University Press, 1983. [4] DOI: 10.1098/rspa.1936.0111 · Zbl 0014.42304 [5] DOI: 10.1098/rspa.1939.0140 · Zbl 0023.43004 [6] Gelrsquo;Fand I.M., Amer. Math. Soc. Transl. 2 pp 207– (1956) [7] Hille E., American Mathematical Society colloquium Publications 31 pp 349– (1965) [8] Mason L.J., Twistor Newsletter 37 pp 1– (1994) [9] Nicolas J.-P., Ann. Inst Henri Poincaré 62 pp 145– (1995) [10] Penrose, R. ”Twistors as spin 3/2 charges Gravitation and modern cosmology”. Edited by: Zichichi, A., de Sabbata, N. and Sánchez, N. 129–137. [11] DOI: 10.1098/rspa.1965.0058 · Zbl 0129.41202 [12] Penrose R, Spinors and space-time Cambridge mongraphs on mathematical physics, Two-spinor calculus and relativistic fields 1 (1984) [13] Penrose R, Spinors and space-time, Cambridge monographs on mathematical physics, Spinor and twistor methods in spacetime geometry 2 (1986) [14] DOI: 10.1103/PhysRev.60.61 · Zbl 0026.28704 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.