Redshift of a compact binary star in the neighborhood of a supermassive black hole

Abstract

We present a method that allows to calculate the redshift of a compact binary star which moves in a strong external gravitational field, e.g. the field of a supermassive black hole. If the binary is close enough to the field center, its motion can be relativistic, while the relative motion of the stars in the binary is still non-relativistic. The latter can be computed in a co-moving reference frame. We calculate the redshift in a co-moving frame in Fermi coordinates as a series in the size of the binary $$\varrho $$ . The obtained expression is written in a covariant form up to linear terms in $$\varrho $$ . Using the equations of motion that have been obtained in a previous paper, we present the method of calculation of the redshift of a sample binary star moving in the field of a black hole. We illustrate this method by numerical model for the case of spherically-symmetric (Schwarzschild) black hole. The method can be applied to the analysis of the timing data of pulsars in the vicinity of the Galactic Center, and to the reconstruction of the binary star motion by its redshift.