On Perturbations of Extreme Kerr-Newman Black Holes and their Evolution

Using black hole inequalities and the increase of the horizon's areas, we show that there are arbitrarily small electro-vacuum perturbations of the standard initial data of the extreme Reissner-Nordstrom black hole that (by contradiction) cannot decay in time into any extreme Kerr-Newman black hole. This proves that, in a formal sense, the reduced family of the extreme Kerr-Newman black holes is unstable. It remains of course to be seen whether the whole family of charged black holes, including those extremes, is stable or not.