The importance of gravitational selffield effects in binary systems with compact objects. I. The ``static twobody problem'' and the attraction law in a postNewtonian 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 postNewtonian 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 postNewtonian approximation and then (in paper II) we shall be concerned with the postpostNewtonian approximation. In both approximations we obtain Newton's attraction forceM _{S1} M _{S2}/R ^{2} plus terms of order 1/R ^{3} and higher, whereM _{S1},M _{S2} are the Schwarzschild masses of the bodies.
 Publication:

General Relativity and Gravitation
 Pub Date:
 September 1978
 DOI:
 10.1007/BF00760870
 Bibcode:
 1978GReGr...9..809R
 Keywords:

 Astronomical Models;
 Gravitational Effects;
 Gravitational Fields;
 Relativity;
 Two Body Problem;
 Approximation;
 Binary Stars;
 Mathematical Models;
 Newton Theory;
 Astrophysics;
 Binaries:Compact Objects