Kaluza-Klein vacuum multi-black holes in five dimensions

We investigate five-dimensional vacuum solutions which represent rotating multiblack holes in asymptotically Kaluza-Klein spacetimes. We show that multiblack holes rotate maximally along extra dimension, and stationary configurations in vacuum are achieved by the balance of the gravitational attraction force and repulsive force caused by the rotations of black holes. We also show that each black hole can have the different topology of the lens space in addition to the spherical topology, and the mass of black holes is quantized by the size of the extra dimension and horizon topology.