Physically Acceptable Solution of Einstein's Equation for Many-Body System

Einstein’s gravitational equation for slowly moving particles is solved up to the order of the post-post-Newtonian approximation. Though in this order the metric tensor diverges at spatial infinity when de Donder’s coordinate condition is employed, it is shown that there exist a class of coordinate systems in which the metric tensor is Minkowskian at infinity. We get solutions for the metric tensor up to the order of c-6. Using these solutions, we obtain, in the post-Newtonian order, the most general Hamiltonian for many-body system. The G·v4-part of the potential in the post-post-Newtonian order is also given.