’s are tensors.
In the theory, as we have described it up to this point, Einstein selected a Cartesian space-time mesh-system, that is to say, a Galilean frame, and he assumed that as measured in this mesh-system the
’s at infinity were to be given by
all other
’s vanishing. These boundary conditions implied that space-time was perfectly flat at infinity, hence satisfied the equation
. It may be realised that we are merely expressing in another way what was said at the beginning of the chapter; the boundary values written above and the flatness of space-time at infinity being equivalent statements. Under these circumstances we saw that the universe could not be finite; we should have the quasi-Euclidean infinite space-time universe.