Equations of hydrodynamics in general relativity in the slow motion approximation

By means of a formal solution to the Einstein gravitational field equations a slow motion expansion in inverse powers of the speed of light is developed for the metric tensor. The formal solution, which satisfies the deDonder coordinate conditions and the Trautman outgoing radiation condition, is in the form of an integral equation which is solved iteratively. A stress-energy tensor appropriate to a perfect fluid is assumed and all orders of the metric needed to obtain the equations of motion and conserved quantities to the 21/2post-Newtonian approximation are found. The results are compared to those obtained in another gauge by S. Chandrasekhar. In addition, the relation of the fast motion approximation to the slow motion approximation is examined.