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Elastic instability of black rings at large D

Using the inverse dimensional expansion method we study the elastic instability of black rings found recently in numerical analysis of fully nonlinear dynamical evolutions. In our analysis we should perform 1/D^1/2 expansions, not usual 1/D expansions, of the Einstein equations to capture this elastic instability of D dimensional black rings. By solving the Einstein equations at large D we obtain the effective equations for black rings, and the perturbation analysis of the large D effective equations with 1/D^1/2 expansions yields the formula for quasinormal mode frequencies. From this formula, we find that black rings actually suffer from both elastic and Gregory-Laflamme like instabilities. These instabilities are coupled and appear at the same time as observed in numerical analysis. The elastic instability does disappear at the infinite limit of a ring radius, which implies that the (boosted) black string is stable to elastic perturbations. Furthermore we observe that the Gregory-Laflamme like instability becomes more efficient than the elastic instability even for certain thin black rings in enough higher dimensions.