Gregory-Laflamme encounters Superradiance

TL;DR

This paper studies how superradiant scattering affects the stability of rotating black strings, revealing a finite-m mode superradiant instability in six-dimensional cases and exploring its relation to Gregory-Laflamme instability.

Contribution

It identifies a new finite-m superradiant instability in six-dimensional rotating black strings and analyzes its interplay with known Gregory-Laflamme instability.

Findings

Rapidly rotating black strings are unstable to superradiant modes within a bounded length range.

Five-dimensional Myers-Perry black holes do not exhibit stable particle orbits, affecting superradiant stability.

The superradiant instability can coexist or compete with Gregory-Laflamme instability depending on parameters.

Abstract

We investigate the effect of superradiant scattering of gravitational perturbations on the stability of rotating black strings, focusing on the six dimensional equal-spinning Myers-Perry black string. We find that rapidly rotating black strings are unstable to gravitational superradiant modes within a bounded range of string lengths. The instability occurs because momentum along the string direction creates a potential barrier that allows for the confinement of superradiant modes. Yet, five dimensional Myers-Perry black holes do not have stable particle orbits so, unlike other known superradiant systems, these black strings remain stable to perturbations with sufficiently high azimuthal mode number -- this is a `finite-$m$' superradiant instability. For some parameters, this instability competes with the Gregory-Laflamme instability, but otherwise exists independently. The onset of this instability is degenerate and branches to multiple steady-state solutions. This paper is the first of a trilogy: in the next two, we construct two distinct families of rotating strings emerging from the superradiant onset (the `black resonator strings' and `helical black strings'). We argue that similar physics is present in 5-dimensional Kerr black strings, but not in $D>6$ equal-spinning Myers-Perry black strings.