LINEAR-STABILITY OF EINSTEIN-SKYRME BLACK-HOLES

We analyze the linear stability of black hole solutions of the Einstein-Skyrme system. These solutions, which we have recently found numerically, provide counter examples to the "no hair" conjecture for black holes of non-linear matter models. We show that there exist only oscillating radial modes (satisfying the necessary boundary conditions at the horizon and at infinity), with the possible exception of a small region of the two-dimensional parameter space of the black hole configurations. Some numerical evidence for non-linear stability is also discussed.