Relativistic effects in many-body systems of finite size,internal structure,and internal motions: I. “Self-acceleration” of astrophysical systems

It is proved that the post-Newtonian general relativistic center of rest mass of a bounded physical system composed of a number of bodies characterized by finite dimensions, arbitrary internal structure, and arbitrary internal motions cannot in general move uniformly, contrary to what was conventionally accepted up to now. Mathematical expressions are derived and discussed describing, in terms of the above characteristics of the bodies, the position and velocity vectors of the center of rest mass of the system and the force, which is responsible for its nonuniform motion, with respect to the uniformly moving post-Newtonian general relativistic center of inertial mass of the physical system. In the special case of a binary star it is shown that the center of rest mass should describe, around the uniformly moving center of inertial mass, an ellipse of the same period and eccentricity as those of the Newtonian elliptical orbit of the relative motion. The length of the axes of this ellipse depends on the internal characteristics of the members of the binary star, and the motion of the center of rest mass becomes important when these characteristics are strong enough. Finally, it is proved that in every effort for describing theoretically a binary system, the internal characteristics of the members of which are ignored, and for accurate measurements of their positions and velocities, the above fictitious motion of the center of rest mass has to be taken into account; otherwise, the results of the measurements will not be consistent with the theoretical predictions.