Torsion and Curvature

Our point of view is quite similar to that of Sergei Feodosin, but in UFT 137 for example it has been shown that the commutator method leads to an antisymmetric connection, simply because the mu and nu indices of the commutator are the same as those of the connection. In papers such as UFT 102 the proof of this method is given in all detail. Torsion cannot be neglected mathematically. The proof I gave in UFT 102 gives all the details omitted by S. P. Carroll in “Spacetime and Geometry: an Introduction to General Relativity” . I agree completely with Sergei Feodosin about the gravitomagnetic field and the gravitational equivalent of the Faraday Law of Induction. The connection cannot be symmetric because in that case, the commutator would be symmetric and therefore zero, in which case both torsion and curvature vanish, and there is no gravitation. Unfortunately, and in my opinion of course, the whole of twentieth century general relativity developed as a subject in which the connection was incorrectly symmetric. It must be antisymmetric. Judging by feedback this opinion of mine has been accepted by almost all intellectuals worldwide. By intellectuals I do not mean academics only. So in our recent book “Criticisms of the Einstein Field Equation” (published by Cambridge International Science Publishing, and very well received by the open minded) we used computer algebra to show that all metrics of the Einstein field equation are internally inconsistent. We base all our ECE work on the corrected geometry (due to Cartan), and this has strengthened general relativity judging by the huge amount of interest in our work.

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