Physical properties of the double-Kerr solution

Abstract

We analysed two special cases of the double-Kerr solution describing a system of two stationary co-axial Kerr black holes, with equal mass and either the same or opposite angular momentum. These cases are asymptotically flat and obey the axis condition, but there is always a strut (i.e. a conical singularity) between the black holes, preventing the collapse of the system. Studying the force associated to the strut, we show that the force between the two black holes is more attractive in the counter-rotating than in the co-rotating case. We also show that, for both the counter-rotating and co-rotating cases, 1) the angular velocity of the two black holes decreases as they approach one another, for fixed mass and angular momentum; 2) the extremal limit J/M2 varies with the distance between the black holes and may even be larger than one. These results are interpreted in terms of rotational dragging effects.