  Black resonators and geons in global AdS are rapidly rotating, low-energy
solutions with a helical Killing field. We study the linear mode stability of
equal angular momenta, five-dimensional black resonators and geons under
scalar, electromagnetic, and gravitational perturbations. We find that black
resonators are unstable to the superradiant instability, in agreement with
previously known results. Perhaps surprisingly, many geons appear linearly
stable, despite having an ergoregion. This apparent stability implies that
geons are important long-lived, low-energy states in the dual gauge theory.
However, we do find that geons are unstable within a certain range of parameter
space. We comment on the nature of this instability and to its possible
endpoints. We also report on new non-spinning oscillating geons, which we
construct within a cohomogeneity two ansatz. Given the existing arguments that
suggest our linear stability results may be extended nonlinearly, our findings
indicate that most geons are generic and long-lived solutions.
