The importance of gravitational self-field effects in binary systems with compact objects. I. The ?static two-body problem? and the attraction law in a post-Newtonian approximation of general relativity

Abstract

As a first step toward a proper treatment of compact objects in binary systems the attraction force of two massive bodies connected by a rod is calculated in a post-Newtonian expansion. Contrary to a calculation by Weyl und Bach we start without specializing the internal structure of the bodies. We consider general anisotropic pressures and do not require axial symmetry for the bodies. We calculate the attraction force first in a post-Newtonian approximation and then (in paper II) we shall be concerned with the post-post-Newtonian approximation. In both approximations we obtain Newton's attraction forceMS1MS2/R2 plus terms of order 1/R3 and higher, whereMS1,MS2 are the Schwarzschild masses of the bodies.