Horizon instability of an extreme Reissner-Nordstrom black hole
Abstract: Recently, a novel instability was found for a massless scalar field on an extreme Reissner-Nordstrom black hole. This instability is a purely classical process, and it makes a part of energy-momentum tensor of the scalar field discontinuous on the horizon at late time. We show that a similar instability occurs also for a massive scalar field and for coupled linearized gravitational and electromagnetic perturbations. These instabilities are intimately related to conserved quantities constructed from perturbative fields. We analytically show the existence of instability based on these quantities when possible, and also conduct numerical analysis to examine more general cases. We discuss the physical mechanism and implications of this instability, and also argue the final fate of the system after nonlinear effects set in.
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