Superradiant instability of large radius doubly spinning black rings

TL;DR

This paper demonstrates that large radius doubly spinning black rings in five dimensions are subject to a superradiant instability, which limits their rotation and influences their stability, providing insights into their dynamical behavior.

Contribution

It identifies and analyzes a superradiant instability in large radius doubly spinning black rings, deriving the frequency spectrum and estimating the rotation bound.

Findings

The instability is active for large radius rings with high S^2 rotation.

The instability provides a dynamical upper bound on black ring rotation.

Higher dimensional black rings are expected to be stable against this mechanism.

Abstract

We point out that 5D large radius doubly spinning black rings with rotation along S^1 and S^2 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 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 timescale of this instability in the black ring background, and show that it is active for large radius rings with large rotation along S^2. We identify the endpoint 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 is being conjectured. They will be stable against this mechanism.