Spontaneous scalarization of charged stars

We study static and spherically symmetric charged stars with a nontrivial profile of the scalar field $\phi$ in Einstein-Maxwell-scalar theories. The is coupled to $U(1)$ gauge $A_{\mu}$ form $-\alpha(\phi)F_{\mu \nu}F^{\mu \nu}/4$, where $F_{\mu \nu}=\partial_{\mu}A_{\nu}-\partial_{\nu} A_{\mu}$ strength tensor. Analogous case black holes, we show that this type interaction can induce spontaneous scalarization under conditions $({\rm d}\alpha/{\rm d}\phi) (0)=0$ d}^2\alpha/{\rm d}\phi^2) (0)>0$. For coupling $\alpha (\phi)=\exp (-\beta \phi^2/M_{\rm pl}^2)$, $\beta~(<0)$ constant $M_{\rm pl}$ reduced Planck mass, there branch star solutions approaching $0$ toward spatial infinity, besides general relativistic vanishing field, i.e., Einstein-Maxwell model. As ratio $\rho_c/\rho_m$ between charge density $\rho_c$ matter $\rho_m$ increases its maximum value, mass $M$ relativity tends be enhanced due increase repulsive Coulomb force against gravity. In regime, appearance branches induced by negative $\beta$ order $-1$ effectively reduces for wide range central densities, leading smaller masses radii comparison those branch. Our analysis indicates not only curvature invariants but also scalar-gauge Einstein