Wikipedia Material on The First and Second Bianchi Identities


This material and associated links are incorrect and out-dated. The so called first and second Bianchi identities used in the obsolete cosmology are not true identities. They are equations which apply if and only if the spacetime torsion is zero and if and only if the connection is symmetric. They are not true in the case of non-zero torsion. The correct and rigorous identity is that due to Cartan. This is proven in many of the ECE papers on this site, starting with paper 15. I often refer to this as the Cartan Bianchi identity. It is a direct consequence of the commutator of covariant derivatives acting on any tensor to give the structures of the curvature and torsion tensors. The Hodge dual of the commutator acts similarly on any tensor to give the Hodge duals of the curvature and torsion tensors. These two Hodge dual tensors are related by the Cartan Evans identity. These are given in more detail in the attached document. The Einstein field equation is based on the incorrect assumption of a symmetric connection and its metrics are in consequence incorrect. This has been known since 2007 and again accepted by the entire scientific readership of ECE. Wikipedia is the only vehicle that does not allow free discussion of these important developments and so Wikipedia is worthless as a description of modern theoretical physics.



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