Integration of Einstein's Equations in the Weak Field Domain Using the   "Einstein" Gauge
  We propose a new alternative gauge for the Einstein equations instead of the de Donder gauge, which allows in the limit of weak fields a straightforward integration of these equations. The Newtonian potential plays a new interesting role in this framework. The calculations are demonstrated explicitely for 2 simple astrophysical models. 
E. Hitzer and H. Dehnen