STABILITY OF EINSTEIN YANG-MILLS BLACK-HOLES

We examine the problem of stability of Einstein Yang-Mills black holes, studied recently by Straumann and Zhou in the framework of linearized perturbation technique. It is pointed out that the existence of the exponentially growing radial mode, found by Straumann and Zhou, does not necessarily signal behaviour at the horizon. In particular, we show that the lowest-energy coloured black hole is linearly stable against radial perturbations. We show also that the SU (2) Reissner-Nordstrom solution with mass M and magnetic charge 1/g is dynamically stable if the dimensionless constant G1/2gM is bigger than some critical value.