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New curvature-torsion relations through decomposition of the Bianchi Identities

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Abstract

The Bianchi Identities relating asymmetric curvature to torsion are obtained as a new set of equations governing second-order curvature tensors. The usual contribution of symmetric curvature to the gravitational field is found to be a subset of these identities though with an added contribution due to torsion gradients. The antisymmetric curvature two-tensor is shown to be related to the divergence of the torsion. Using a model of particle-antiparticle pair production, identification of certain torsion components with electroweak fields is proposed. These components obey equations, similar to Maxwell's, that are subsets of these linear Bianchi identities. These results are shown to be consistent with gauge and other previous analyses.

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Authors and Affiliations

  1. CIRES, University of Colorado, 80309, Boulder, Colorado

    John B. Davies

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  1. John B. Davies
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Davies, J.B. New curvature-torsion relations through decomposition of the Bianchi Identities. Found Phys 18, 563–569 (1988). https://doi.org/10.1007/BF00732746

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  • DOI: https://doi.org/10.1007/BF00732746

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