Post-Newtonian two-body and n-body problems with electric charge in general relativity

Starting with the Bazanski two-body post-Newtonian Lagrangian with electric charge in general relativity, we construct a coordinate transformation (not involving center-of-mass coordinates) with two arbitrary parameters and obtain a Hamiltonian which is in agreement with one derived from quantum field theory. The field theory Hamiltonian corresponds to using an arbitrary parameter x/sub p/ in the photon propagator as well as an arbitrary parameter x/sub g/ in the graviton propagator. These results are also generalized to the case of n bodies. The condition for static balance e/sub i/= +- G1/2m/sub i/ is found to hold both for the exact Reissner--Nordstrom ''one-body'' problem and for the post-Newtonian n-body problem. An alternate condition for static balance e/sub i/= +- (Gm1m2)/sup 1/2/ is found to hold for the post-Newtonian two-body problem. The precession of the perihelion for the post-Newtonian two-body problem is given along with four special cases, one of which is the two-body generalization of the ''one-body'' special relativity result of Sommerfeld. Post-Newtonian two-body equations of motion (in center-of-mass coordinates) with the condition of static balance are also examined