Exact formation of hairy planar black holes

Abstract

We consider Einstein gravity minimally coupled to a scalar field with a given potential in general dimensions. We obtain large classes of static hairy planar black holes which are asymptotic to AdS space-times. In particular, for a special case $\mu=(n-2)/2$, we obtain new classes of exact dynamical solutions describing black holes formation. We find there are two classes of collapse solutions. The first class solutions describe the evolution start from AdS space-time with a naked singularity at the origin. The space-time is linearly unstable and evolves into stationary black hole states even under small perturbation. The second class solutions describe the space-time spontaneously evolves from AdS vacua into stationary black hole states undergoing non-linear instability. We also discuss the global properties of all these dynamical solutions.