Spontaneous scalarization of a conducting sphere in Maxwell-scalar models

We study the spontaneous scalarization of a standard conducting charged sphere embedded in Maxwell-scalar models flat spacetime, wherein scalar field $\phi$ is nonminimally coupled to Maxwell electrodynamics. This setup serves as toy model for (vacuum) black holes Einstein-Maxwell-scalar (generalized scalar-tensor) models. In case, unlike hole cases, closed-form solutions exist scalarized configurations. compute these configurations three illustrations nonminimal couplings: one that \textit{exactly} linearizes equation, and remaining two produce nonlinear continuations first one. show former leads runaway behaviour regions parameter space neither Coulomb nor are stable model; but latter can heal this producing dynamically preferred over parallels reports on extended-scalar-Gauss-Bonnet Moreover, we analyse impact choice boundary conditions phenomenon. Dirichlet Neumann accommodate both (linearly) unstable regions, scalar-free sphere; radiative always yield an solution preference scalarization. Finally, perform numerical evolution full system, following process. They confirm linear stability analysis reveal phenomenon occur qualitatively distinct ways.