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. Any cosmological model resulting in a "partially" degenerate metric where g[not equal to = 0 is neither a relativistic cosmological model nor 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,
It is not an Einstein universe. On (8) and (8b) the ratio,
This is a line-element which cannot describe an Einstein universe. The Einstein space described by (28) consists of only one "world line", through the point,
This line-element cannot describe an Einstein universe. The Einstein space described by (37) consists of only one point:
This is not an Einstein universe. The radius of curvature of (54) is,
George Bernard Shaw declared to radio listeners that Newtonianism "had crumpled up and was succeeded by the Einstein universe
." But Newton had left openings for the relativists to follow, and Einstein did not presume to dismiss him: "Let no one suppose," he said in 1919, "that the mighty work of Newton can really be superseded by this or any other theory.