Superradiant instability of large radius doubly spinning black rings

We point out that 5D large radius doubly spinning black rings with rotationalong S^1 and S^2 are afflicted by a robust instability. It is triggered bysuperradiant bound state modes. The Kaluza-Klein momentum of the mode along thering is responsible for the bound state. This kind of instability in blackstrings and branes was first suggested by Marolf and Palmer and studied indetail by Cardoso, Lemos and Yoshida. We find the frequency spectrum andtimescale of this instability in the black ring background, and show that it isactive for large radius rings with large rotation along S^2. We identify theendpoint of the instability and argue that it provides a dynamical mechanismthat introduces an upper bound in the rotation of the black ring. To estimatethe upper bound, we use the recent black ring model of Hovdebo and Myers, witha minor extension to accommodate an extra small angular momentum. Thisdynamical bound can be smaller than the Kerr-like bound imposed by regularityat the horizon. Recently, the existence of higher dimensional black rings isbeing conjectured. They will be stable against this mechanism.Comment: 21 pages, 3 figures. Overall minor improvements in discussions added. Matches published version in PR