Relativity and Cosmology


Remarks on Mӧller Mistaken Famous Paper from 1943

Authors: Jaykov Foukzon

Einstein field equations was originally derived by Einstein in 1915 in respect with canonical formalism of Riemann geometry,i.e. by using the classical sufficiently smooth metric tensor, smooth Riemann curvature tensor, smooth Ricci tensor,smooth scalar curvature, etc.. However have soon been found singular solutions of the Einstein field equations with degenerate and singular metric tensor and singular Riemann curvature tensor. These degenerate and singular solutions of the Einstein field equations was formally accepted by main part of scientific community beyond rigorous canonical formalism of Riemannian geometry.Recall that the classical Cartan’s structural equations show in a compact way the relation between a connection and its curvature, and reveals their geometric interpretation in terms of moving frames. In order to study the mathematical properties of singularities, we need to study the geometry of manifolds endowed on the tangent bundle with a symmetric bilinear form which is allowed to become degenerate (singular). But if the fundamental tensor is allowed to be degenerate (singular), there are some obstructions in constructing the geometric objects normally associated to the fundamental tensor. Also, local orthonormal frames and co-frames no longer exist, as well as the metric connection and its curvature operator [2].As an important example of the geometry with the fundamental tensor which is allowed to be degenerate, we consider now Mӧller’s uniformly accelerated frame given by Mӧller’s line element

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[v1] 2019-07-07 12:01:37

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