Systematic approximations in the calculation of gravitational fields

Abstract

The determination of Newtonian gravitational fields is of trivial simplicity in comparison with corresponding relativistic problems. To find the Newtonian potential we do not have to solve any differential equation; it is given as an integral taken over the instantaneous mass distribution, and any difficulties there may be arise merely in evaluating the integral. In giving the well-known retarded-potential formula, Einstein (1916) took the first step towards the systematic calculation of relativistic gravitational fields. But it is only a first approximation, leaving in what purports to be empty space a residual energy tensor which is uncomfortably large. Further, the usual derivation of the retarded potential formula does not seem to open the way to higher approximations.