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:::::Hi MatthewQ, Are you sure about non Riemannian as well (degenerate, meaning vanishing determinant)? How do you diagonalize it then? Mine is degenerate just to avoid possibility of diagonalization, according to Einstein's demand of non symmetric metric that Misner, Thorne, and Wheeler forgot to put into their bibliography and also to discuss it while talking about Einstein's ideas <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', ''"Scientific American"'', April 1950.</ref>. [[User:JimJast|JimJast]] 19:59, 21 August 2011 (EDT)
:::::Hi MatthewQ, Are you sure about non Riemannian as well (degenerate, meaning vanishing determinant)? How do you diagonalize it then? Mine is degenerate just to avoid possibility of diagonalization, according to Einstein's demand of non symmetric metric that Misner, Thorne, and Wheeler forgot to put into their bibliography and also to discuss it while talking about Einstein's ideas <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', ''"Scientific American"'', April 1950.</ref>. [[User:JimJast|JimJast]] 19:59, 21 August 2011 (EDT)
:::::: Metrics on psudeo-Riemannian manifolds are symmetric. Just think about the Minkowski metric: diag(-1,+1,+1,+1). These metrics satisfy all the usual axioms of a metrics except for positive definite. That is, it can be negative or zero for non-identical points. They also have to be non-degenerate, so whatever it is you're defining isn't a metric or even a pseudo-metric.
:::::: I don't have access to the article you mentioned, but I really doubt Einstein demanded a non symmetric metric. Can you provide a quote? Regardless, do you know what a metric is? Roughly speaking, it's something to measure distance between points A and B. So when you say your "metric" is not symmetric you're saying that the distance from A to B is not the same as the distance from B to A. --[[User:MatthewQ|MatthewQ]] 22:04, 21 August 2011 (EDT)
==References==
==References==