A remark about wave equations on the extreme Reissner-Nordstr\"om black   hole exterior
  We consider a massless scalar field propagating on the exterior of the extreme Reissner-Nordstr\"om black hole. Using a discrete conformal symmetry of this spacetime, we draw a one-to-one relationship between the behavior of the field near the future horizon and near future null infinity. In particular, we show that the polynomial growth of the second and higher transversal derivatives along the horizon, recently found by Aretakis, reflects well known facts about the retarded time asymptotics at null infinity. 
Piotr Bizo\'n and Helmut Friedrich
gr-qc