We show that the asymptotically flat hairy black holes, solutions of the Einstein field equations minimally coupled to a scalar field, previously discovered by one of us, present mode instability against linear radial perturbations. It is also shown that the number of unstable modes is finite and their frequencies can be made arbitrarily small.

• Received 9 July 2013

DOI:https://doi.org/10.1103/PhysRevD.88.064011