Geodesic motion in a stationary dihole spacetime

The knowledge of the properties of the different exact solutions modeling binary systems is a necessary step toward the classification of physically suitable solutions and its corresponding limits of applicability. In the present paper, we perform an analysis of the geodesics around two counter-rotating Kerr-Newman black holes endowed with opposite electric charges, which achieve equilibrium by means of a strut between their constituents. We find that bounded and unbounded orbits are possible. However, test particles may cross between the black holes only if their angular momentum equals zero; otherwise, there exists a repulsive potential, which prohibits such orbits. Two important aspects are pointed out for these trajectories: (i) the motion of photons is affected once it has crossed the strut, and (ii) massive particles exhibit oscillatory motion, as a first analog of the Sitnikov problem in general relativity. The radius of the innermost stable circular orbit as a function of the physical parameters of the black holes is also investigated.