Superradiant instability of large radius doubly spinning black rings

We point out that 5D large radius doubly spinning black rings with rotation along S1 and S2 are afflicted by a robust instability. It is triggered by superradiant bound state modes. The Kaluza-Klein momentum of the mode along the ring is responsible for the bound state. This is shown by analyzing the boosted Kerr black string. The present kind of instability in black strings and branes was first suggested by Marolf and Palmer and studied in detail by Cardoso, Lemos and Yoshida. We find the frequency spectrum and time scale of this instability in the black ring background, and show that it is active for infinite-radius rings with large rotation along S2. We identify the end point of the instability and argue that it provides a dynamical mechanism that introduces an upper bound in the rotation of the black ring. To estimate the upper bound, we use the recent black ring model of Hovdebo and Myers, with a minor extension to accommodate an extra small angular momentum. This dynamical bound can be smaller than the Kerr-like bound imposed by regularity at the horizon. Recently, the existence of higher-dimensional black rings has been conjectured. They will be stable against this mechanism