Abstract
We study the stationary asymptotically flat five-dimensional vacuum solution describing black di-ring: two concentric black rings. We give an outline of solution generating methods to construct the black di-ring and introduce the rod structures of the black di-ring and the seed solutions. We investigate the phase structure of black di-ring to show the infinite non-uniqueness of the solution. We analyze the distributions of black di-rings whose Komar angular momentum of inner ring vanishes and whose angular velocity of inner ring vanishes in the phase diagram. We also investigate temperatures of horizons for these two special families to consider the existence of the thermal equilibrium black di-rings.
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