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A new algorithm for computing the accurate values of quasinormal frequencies of extremal Reissner-Nordström black holes is presented. The numerically computed values are consistent with the values earlier obtained by Leaver and those obtained through the WKB method. Our results are more precise than other results known to date. We also find a curious fact that the resonant frequencies of gravitational waves with multi-pole index l coincide with those of electromagnetic waves with multi-pole index l − 1 in the extremal limit.

We show that the S 1 -rotating black rings can be superposed by the solution generating technique.We analyze the black di-ring solution for the simplest case of multiple rings. There exists an equilibrium black di-ring where the conical singularities are cured by the suitable choice of physical parameters. Also there are infinite numbers of black di-rings with the same mass and angular momentum. These di-rings 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 di-ring solutions.