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. *
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.
The method of calculation of redshift of light from a point-like source that moves in the gravitational field of the Kerr black hole as a function of time of observation is developed. The widely presented in literature methods for solving the boundary problem are based on a numerical selection of parameters of geodesics. In contrast, the proposed method is based on approximate analytical expressions for isotropic geodesics in the Kerr metric. The proposed method is illustrated by the example of a model problem with parameters corresponding to real stars moving in the immediate vicinity of a supermassive black hole located in the Center of our Galaxy. The same example shows the efficiency and good accuracy of this method.
The general problem of calculating of the propagation of electromagnetic radiation from particles or stars moving in the vicinity of a supermassive black hole is considered in geometrical optics approximation within the framework of the general theory of relativity. Different approaches that can be used to calculate certain characteristics of radiation, including redshift, the intensity and rotation of the plane of polarization, which have been presented in the literature are analysed herein. The inverse problem—the calculation of the parameters of the motion of the source (star or particle) from the data of the redshift, the intensity and the plane of polarization—is also considered.
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