The Equations of Motion of Compact Binaries in the Neighborhood of Supermassive Black Hole

摘要

By the use of Einstein-Infeld-Hoffmann method, the equations of motion of a binary star system in the field of a supermassive black hole are derived. In spite of the fact that the motion of a binary system as a whole can be relativistic or even ultra-relativistic with respect to the supermassive black hole, it is shown, that under the assumption of non-relativistic relative motion of the stars in binary system, the motion of the binary system as a whole satisfies the Mathisson-Papapetrou equations with additional terms depending on quadrupole moments. Exemplary case of ultrarelativistic motion of a binary neutron star in the vicinity of non-rotating black hole is considered. It it shown that the motion of binary's center of mass may considerably differ from geodesic motion.