Equivalence of vacuum Yang-Mills gravitation and vacuum Einstein gravitation.

Physics

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Gravitation Theory

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In the Yang-Mills formulation of gravitational dynamics based uponSL(2,C) spin transformations acting on Dirac spinors, the vacuum field equations are ζR κα +C κρασ R ρσ = 0 and andtriangledown _{left[ {kappa ^R λ } right]v} = 0. HereR κα is the Ricci curvature andC μκαν is the Weyl conformal curvature; ξ is a coupling constant. We show the equivalence between solutions of these equations and the vacuum Einstein equationsR κα = 0. The proof uses the Newman-Penrose formalism.

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