Horizon instability of extremal Reissner-Nordstr\"om black holes to   charged perturbations
  We investigate the stability of highly charged Reissner-Nordstr\"om black holes to charged scalar perturbations. We show that the near-horizon region exhibits a transient instability which becomes the Aretakis instability in the extremal limit. The rates we obtain match the enhanced rates for nonaxisymmetric perturbations of the near-extremal and extremal Kerr solutions. The agreement is shown to arise from a shared near-horizon symmetry of the two scenarios. 
Peter Zimmerman
gr-qc