Self Consistency of Riemann Geometry

Feed: Dr. Myron Evans
Posted on: Thursday, June 23, 2011 11:19 AM
Author: metric345
Subject: Self Consistency of Riemann Geometry

I evaluated the mu = nu = 1 condition in note 186(7), giving eq. (8). In my opinion, the way to interpret that equation is that metric compatibility contradicts the commutator method. The former gives a finite gamma sup 1 sub 11 and the latter shows that a gamma sup 1 sub 11 leads to zero torsion and curvature and a flat spacetime and a zero gamma sup 1 sub 11. So I concluded that for any g sub 11, eq. (9) has no meaning and metric compatibility can only be used with an antisymmetric connection, otherwise Riemann geometry itself is self inconsistent. The SM gives an accurate description of the relativistic Kepler problem, so cannot be abandoned. In the latest note I suggested a perturbation of the SM, and it works fine.

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