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On irreducible partials of Ricci tensor traceless part in finite space-time region in GR

Yu. Semenov
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Abstract

Riemann tensor irreducible part $E_{iklm} = {1/2} (g_{il}S_{km} + g_{km}S_{il} - g_{im}S_{kl} - g_{kl}S_{im})$ constructed from metric tensor $g_{ik}$ and traceless part of Ricci tensor $S_{ik} = R_{ik} - {1/4} g_{ik} R$ is expanded into bilinear combinations of bivectorial fields being eigenfunctions of $E$. Field equations for the bivectors induced by Bianchi identities are studied and it is shown that in general case it will be 3-parametric local symmetry group Yang-Mills field.

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Yu. Semenov. 2003-03-25. On irreducible partials of Ricci tensor traceless part in finite space-time region in GR. https://arxiv.org/abs/gr-qc/0303098

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