does John Baez do that here
or maybe Sean Carroll does that here
i think they can derive the inverse-square relationship (or maybe it's a 1/r relationship for potential energy) for the flat space-time limit. the constant of proportionality in the Einstein equation ([itex]8 \pi G[/itex]) does
come about to be compatible with Newtonian gravitation.
i can't actually do the math myself (i am ashamed to confess i never figured out tensors), but it appears that this is what they do.