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Now to explain the redshift in the original static Einstein spacetime; $S^3(R)\times\mathbf{R}$ with the obvious Lorentzian metric with proper time in the second factor: the frequency-wavelength relationship is not the same as in flat space.  To see this, consider waves on a circle versus a sphere.  The eigenvalues of Laplacian (for standing waves) are $Cn^2$ versus $C n(n+2)$.  Suppose they are the latter and you assume the former was the case.  Then there will be a discrepancy in the wavelengths that accumulates proportional to the distance.  This is what is happening with the observed redshifts.  So the redshift is a MATHEMATICAL ARTIFACT of ignoring curvature of a static spherical universe and not a physical feature at all.  This is my explanation of the redshift.  It differs from the steady state Fritz Zwicky tired light explanation which says that light traveling over long distances get absorbed and re-emitted by dust.  I don’t think that is what’s going on because there is no blurring (standard big bang critique).