Horizon Instability of Extremal Black Holes
  We show that axisymmetric extremal horizons are unstable under linear scalar perturbations. Specifically, we show that translation invariant derivatives of generic solutions to the wave equation do not decay along such horizons as advanced time tends to infinity, and in fact, higher order derivatives blow up. This result holds in particular for extremal Kerr-Newman and Majumdar-Papapetrou spacetimes and is in stark contrast with the subextremal case for which decay is known for all derivatives along the event horizon. 
Stefanos Aretakis
gr-qc math.AP math.DG