Critical Phenomena in Dynamical Scalarization of Charged Black Holes

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 $T\ensuremath{\propto}\ensuremath{-}\ensuremath{\gamma}\mathrm{ln}|p\ensuremath{-}{p}_{*}|$. 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 ${M}_{p}\ensuremath{-}{M}_{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\propto}|p\ensuremath{-}{p}_{*}{|}^{{\ensuremath{\gamma}}_{\ifmmode\pm\else\textpm\fi{}}}$, where ${M}_{\ifmmode\pm\else\textpm\fi{}}$ are the masses of the scalarized and bald BHs, respectively, when $p\ensuremath{\rightarrow}{p}_{*}$ from above or below, and ${\ensuremath{\gamma}}_{\ifmmode\pm\else\textpm\fi{}}$ the corresponding exponents.