Critical phenomena in dynamical scalarization of charged black hole

We report a new black hole scalarization mechanism and disclose novel dynamical critical phenomena in the process of the nonlinear accretion of the scalar field into black holes. The accretion process can transform a seed black hole into a final scalarized or bald black hole, depending on the initial parameter of the scalar field $p$. There is a critical parameter $p_{\ast}$ and near it all intermediate solutions are attracted to a critical solution and stay there for a time scaling as $T\propto-\gamma\ln|p-p_{\ast}|$. At late times, the solutions evolve into scalarized black holes if $p>p_{\ast}$, or bald black holes if $p<p_{\ast}$. The final masses of the resulting scalarized/bald black holes satisfy power-laws $M_{p}-M_{\pm}\propto|p-p_{\ast}|^{\gamma_{\pm}}$ where $M_{\pm}$ are the masses of the scalarized/bald black holes when $p\to p_\ast$ from above/below, and $\gamma_{\pm}$ the corresponding exponents.