I may have rushed to judgement. Perhaps the correct proceedure is given in Hakim´s An Introduction to Relativistic Gravitation on p. 161. What is used is referred to as the Newtonian approximation. The metric tensor is approximated by making a first order correction to the Minkowski metric. Then the geodesic equation is fitted to Newton's equation of motion. The correction to g(0,0) is then equalvalent to twice the potential energy divided by the mass energy. Here I have used coordinated in lieu of subscripts. I am definitely going to have to get a complete version of MS Word.