vanished and the gravitational equations reduced to
or, what comes to the same thing, to
this last equation being compatible with perfect flatness of space-time (
). Einstein had assumed that this condition of perfect flatness existed at infinity, and it was when this supplementary condition was taken into consideration that Einstein’s law of gravitation became determinate. This was the law which enabled him to anticipate the double bending of a ray of light, the Einstein shift-effect, as also to account for the curious motion of the planet Mercury.
It is obvious that a law of gravitation which entails the existence of perfectly flat space-time at infinity must of necessity lead to an unclosed space-time universe; and so we see that with Einstein’s original gravitational equations, a finite self-contained universe cannot exist. We are thus led to consider how it would be necessary to modify these equations for a finite universe to be realised.
Now we mentioned, when discussing the law of gravitation, that the inclusion of an additional tensor