Dynamical and thermodynamical aspects of interacting Kerr black holes

We consider the asymptotically flat double-Kerr solution for two equal mass black holes with either the same or opposite angular momentum and with a massless strut between them. For fixed angular momentum and mass, the angular velocity of two corotating Kerr black holes decreases as they approach one another, from the Kerr value at infinite separation to the value of a single Kerr black hole with twice the mass and the angular momentum at the horizons merging limit. We show that the ratio J/M{sup 2} for extremal corotating Kerr black holes varies from unity at infinite separation to two at the merging limit. These results are interpreted in terms of rotational dragging and compared with the case of counterrotating Kerr black holes. We then analyze the merging of ergoregions. In the corotating case the merger point occurs at an angle of {pi}/2, in agreement with recent general arguments. In the counterrotating case the ergoregions never merge. We study the horizon geometry for both cases as a function of the distance and provide embedding diagrams. Finally, we study the thermodynamical evolution of the corotating double-Kerr system, showing that, in the canonical ensemble, it is thermodynamically stable for fast spinning black holes. As for single Kerr black holes the stable and unstable phases are separated by a second order phase transition. We show that for large fixed angular momentum two Kerr black holes reach a minimum distance, before horizon merging has occurred, where the thermodynamical approximation breaks down. We also consider the microcanonical ensemble to study the maximal energy that can be extracted from the double-Kerr system as a function of the separation between the black holes.