Equivalence of vacuum Yang-Mills gravitation and vacuum Einstein gravitation |
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| Authors: | George Debney Edward E. Fairchild Jr. Stephen T. C. Siklos |
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| Affiliation: | (1) Mathematical Institute, Oxford University, OX1 3LB Oxford, England;(2) Present address: Department of Mathematics, Virginia Polytechnic Institute and State University, 24061 Blacksburg, Virginia;(3) Department of Astrophysics, Oxford University, OX1 3RQ Oxford, England;(4) Present address: McDonnell Center for the Space Sciences, Washington University, 63130 St. Louis, Missouri;(5) Department of Astrophysics, Oxford University, OX1 3RQ Oxford, England |
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| Abstract: | In the Yang-Mills formulation of gravitational dynamics based uponSL(2,C) spin transformations acting on Dirac spinors, the vacuum field equations are  R  +C  R = 0 and and![$$triangledown _{left[ {kappa ^R lambda } right]v} = 0$$](/content/tlx33n26274002g8/10714_2004_Article_BF00759647_TeX2GIFIE1.gif) . HereR is the Ricci curvature andC  is the Weyl conformal curvature;  is a coupling constant. We show the equivalence between solutions of these equations and the vacuum Einstein equationsR = 0. The proof uses the Newman-Penrose formalism.Supported by a NATO fellowship.Supported by a SRC fellowship. |
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