The stability of a hypothetical binary at the galactic center

The paper deals with the stability of a hypothetical binary system of black holes in the galactic nucleus (Kardashev's model). On the assumption that the rotation of the pair is in steady state synchronized with that of the surrounding stellar system, the two cases have been studied: 1) the pair is within a homogeneous triaxial ellipsoid; 2) each of the mass points is surrounded by its own sphere which are not overlapping. It is shown that in the first case the binary is dynamically stable if both components are on the principal axis of the ellipsoid and their centers of gravity coincide. In the second case which describes a certain general tendency in the variation of the stability nature, when considering heterogeneous models. The binary is constantly dynamically stable. It is actually always stable in the secular aspect as well.