On the reconstruction of motion of a binary star moving in the external gravitational field of Kerr black hole by its redshift

TL;DR

This paper develops a method to reconstruct the motion of a binary star near a Kerr black hole using redshift data, applicable even close to the event horizon, and demonstrates its effectiveness through numerical modeling.

Contribution

It introduces a novel inverse problem solution for determining binary star motion from redshift measurements in strong gravitational fields.

Findings

Method successfully reconstructs binary motion from redshift data.

Applicable to regions near the black hole's event horizon.

Validated with numerical simulations of galactic center conditions.

Abstract

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.