In terms of the required physical meaning of General Relativity I shall call a spacetime associated with a non-degenerate metric, an Einstein universe, and the associated metric an Einstein metric.
Thus, any "partially" degenerate metric where g[not equal to]0 is not an Einstein metric, and the associated space is not an Einstein universe.
If the required form (3) is relaxed, in which case the resulting metric is non-Einstein, and cannot therefore describe an Einstein universe, (8) can be written as,
Their line-elements therefore cannot describe any Einstein universe.
This is a line-element which cannot describe an Einstein universe.
This line-element cannot describe an Einstein universe.
Furthermore, metric (55) cannot represent an Einstein universe and therefore has no cosmological meaning.