Black diring and infinite nonuniqueness

We show that the $S^1$-rotating black rings can be superposed by the solution-generating technique. We analyze the black diring solution for the simplest case of multiple rings. There exists an equilibrium black diring where the conical singularities are cured by the suitable choice of physical parameters. Also there are infinite numbers of black dirings with the same mass and angular momentum. These dirings can have two different continuous limits of single black rings. Therefore, we can transform the fat black ring to the thin ring with the same mass and angular momentum by way of the diring solutions.