Suppose two black holes where rotating around each other, perhaps spinning into each other, at a distance such that their event horizons merge into one event horizon. It seems to me that the event horizon of the combined objects would, for at least a short while, enclose only one barbell region of space. This event horizon would not be spherical. Is this typical of black holes? Are event horizons in reality not oblate spheres? And does that tell us something about the distribution of mass on the inside of the black hole?