Critical Phenomena in Dynamical Scalarization of Charged Black Holes.

Abstract

We report a new black hole (BH) scalarization mechanism and disclose novel dynamical critical phenomena in the process of the nonlinear accretion of the scalar field into BHs. The accretion process can transform a seed BH into a final scalarized or bald BH, depending on the initial parameter of the scalar field p. There is a critical parameter p_{*} and near it all intermediate solutions are attracted to a critical solution (CS) and stay there for a time scaling as T∝-γln|p-p_{*}|. At late times, the solutions evolve into scalarized black holes (BHs) if p>p_{*}, or bald BHs if p<p_{*}. The final masses of the resulting scalarized-bald BHs satisfy power laws M_{p}-M_{±}∝|p-p_{*}|^{γ_{±}}, where M_{±} are the masses of the scalarized and bald BHs, respectively, when p→p_{*} from above or below, and γ_{±} the corresponding exponents.