**Subject:** Metrics with Finite Energy Momentum Density

**Date:** Sun, 22 Mar 2009 05:37:41 EDT

It is known that these metrics all fail the test of the dual identity, and all use the incorrect symmetric connection symmetry. The new metric condition of paper 128 does not use a connection at all, because the connections cancel out (see notes for paper 128). The condition contains only the ordinary derivative, not the covariant derivative, despite the fact that it is a condition derived from Cartan’s geometry in non-flat space-times. I am surprised that it has been missed by 150 years mathematicians, including Riemann, Christoffel, Ricci, Bianchi and Levi-Civita, probably because they used mathematics that have become more and more abstract, so only a tiny number of mathematicians know it. It seems to me that they too often do not know what they are doing. The complexity of the standard model is why wool was pulled over many eyes in the twentieth century. Wool is a product of sheep-like adherence to incorrect ideas. Even worse is the deliberate falsification of hyper-complicated mathematics used to keep obsolete ideas afloat, part of the familiar shoot the messenger mentality of human nature. The messenger is simple logic.

I implemented the new test in the Maxima program and investigated all metrics with non-diagonal elements. It should be noted that diagonal metrics automatically fulfil this condition since the contravariant metric elements then are the inverse of the covariant ones, giving a constant for the sum in the new condition

partial sub mu g sup nu lambda * g sub lambda rho

for each tripel (mu, nu, rho). I checked this with a number of diagonal metrics. For the non-diagonal metrics the condition was always met, there was no irregularity. In detail the following metrics were tested: M09 Spherically symmetric line element with off-diagonal elements M23* Kerr M27* Goedel M41 Eddington-Finkelstein M65* Alcubierre M73 Anti-Mach metric of plane waves hf homogeneous vacuum (vacuum metric) M74* Petrov M76* homogeneous non-null e-m Fields, type 2 M78* homogeneous perfect fluid, Cartesian M79* Petrov type N M91* Collision of plane waves

(The numbers are irrelevant, is my internal numbering). The details can be looked up in the Cambridge University book, this could be referenced in the paper.

Horst

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