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Abstract. 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.

We present a research of the time evolution of the redshift of light received from the binary star that moves in the external gravitational field of Kerr black hole. We formulate a method for the solution of inverse problem: calculating of the parameters of relative motion of stars in binary system using the redshift data. The considered formalism has no restrictions on the character of the motion of the center of mass of a compact binary star and can be applied even in the case of binary motion close to the event horizon of a supermassive black hole. The efficiency of the method is illustrated on a numerical model with plausible parameters for the binary systems and for the supermassive black hole, which is located in the center of our Galaxy. *

For more than 40 years E.Schmutzer has developed a new approach to the (5-dimensional) projective relativistic theory which he later called Projective Unified Field Theory (PUFT). In the present paper we introduce a new axiomatics for Schmutzer's theory.By means of this axiomatics we can give a new geometrical interpretation of the physical concept of the PUFT.

A compact binary star that moves in a strong external gravitational field of a Schwarzschild black hole is considered. Decomposition of the redshift into a series with respect to the size of the binary system is obtained. This expression is used to calculate the redshift for a model binary system. Possible application of the results is discussed.