Lifetime of unstable hairy black holes

During the last two decades solutions of black holes with various types of “hair” have been discovered. Remarkably, it has been established that many of these hairy black holes are unstable—under small perturbations the hair may collapse. While the static sector of theories admitting hair is well explored by now, our picture of the dynamical process of hair-shedding is still incomplete. In this Letter we provide an important ingredient of the nonlinear dynamics of hair collapse: we derive a universal lower bound on the lifetime of hairy black holes. It is also shown that the amount of hair outside of a black-hole horizon should be fundamentally bounded.