An approximation method to solve Einstein's field equations on a curved background metric

An approximation method is developed to calculate the gravitational field of a matter sourceT moving on a curved background metric that is an exact solution of the field equations and deviates only weakly from flat space-time. The fieldh of the sourceT is supposed to be much smaller than the curved part of the background, so that in the series expansion ofh each order can be expanded in powers of the background.