Diversity of higher dimensional black holes

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We investigated the properties of vacuum solution which describes a pair of rotating black holes on a Kaluza-Klein bubble. We verified the equivalence of the two different solution sets of the black di-ring which were derived by solitonic techneques. We analyzed the phase diagram of black di-ring and showed that the existence of the black di-ring in thermodynamic equilibrium and analyzed the physical properties of it. We confirmed that the black di-ring in thermodynamic equilibrium has no locally stable state.