ÃÛÌÒTV

Recently, a novel instability was found for a massless scalar field on an extreme Reissner-Nordstrom (RN) black hole. This instability is a classical one, and it makes the energy-momentum tensor of the scalar field discontinuous on the horizon at late time. We study the nonlinear evolution of this instability for spherically symmetric perturbations. We find that the endpoint of the instability is generically a non-extreme RN solution, while there exist fine-tuned initial perturbations for which the instability never decays. We discuss the physical mechanism and implications of this instability.