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We give a pedagogical introduction into an old, but unfortunately not commonly known formulation of GR in terms of self-dual two-forms due to in particular Jerzy Plebanski.
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1960
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1962
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A. H. Taubes, “The Riemann-Christoffel Tensor and Tetrad and Self-dual Formalisms”, in Perspectives in Geometry (Essays in honor of V. Hlavaty), ed. Hoffmann, Indiana University Press, pp. 360-368 (1966)
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M. Cahen, R. Debever and L. Defrise, “A complex Vectorial Formalism in General Relativity”, J. Math. Mech. 16
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W. Israel, “Differential forms in general relativity”, Comm. Dublin Inst. Adv. Studies, Ser. A, 19
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C. H. Brans, “Complex Structures And Representations Of The Einstein Equations,” J. Math. Phys. 15
1974
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J. F. Plebanski, “On the separation of Einsteinian substructures,” J. Math. Phys. 18
1977
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M. F. Atiyah, N. J. Hitchin and I. M. Singer, “Selfduality In Four-Dimensional Riemannian Geometry,” Proc. Roy. Soc. Lond. A 362
1978
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R. Penrose and W. Rindler, “Spinors And Space-Time. 1. Two Spinor Calculus And Relativistic Fields,” Cambridge, Uk: Univ. Pr. (1984) 458 P. (Cambridge Monographs On Mathematical Physics)
1984
Cited alongside, same era.
A. Ashtekar, “New Hamiltonian Formulation of General Relativity,” Phys. Rev. D 36
1987
Cited alongside, same era.
Arthur I. Besse, “Einstein Manifolds”, Springer-Verlag, 1987
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T. Jacobson and L. Smolin, “Covariant Action for Ashtekar’s Form of Canonical Gravity,” Class. Quant. Grav. 5
1988
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R. Capovilla, T. Jacobson, J. Dell and L. Mason, “Selfdual two forms and gravity,” Class. Quant. Grav. 8
1991
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A. Z. Petrov, “The classification of spaces defining gravitational fields” (in Russian), Scientific Proceedings pf Kazan State University named after V. I. Ulyanov-Lenin 114
2000
Later among the works it cites.
P. Jordan, J. Ehlers and W. Kundt, “Strenge Lösungen der Feldgleichungen der Allgemeinen Relativitätstheorie”, Akademie der Wissenschaften and der Literatur, Abhandlungen der Mathematisch-naturwissenschaftliche Klasse, Nr 2 pp-21-105 (1960); English translation published in Gen. Rel. Grav. 41
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