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

我们研究静态和球对称带电恒星，其具有爱因斯坦-麦克斯韦标量理论中标量场ϕ的非平凡轮廓。标量场耦合到一个$你(1)$ 规范场 ${\mathrm{一种}}_{\mu }$ 用表格 $-\alpha (\phi )F_{\mu \nu }{F}^{\mu \nu }/4$， 在哪里 $F_{\mu \nu }={\partial }_{\mu }{\mathrm{一种}}_{\nu }-{\partial }_{\nu }{\mathrm{一种}}_{\mu }$是场强张量。类似于带电黑洞的情况，我们表明这种类型的相互作用可以在以下条件下诱导带电恒星的自发标量化$(\mathrm{d}\alpha /\mathrm{d}\phi )(0)=0$ 和 $({\mathrm{d}}^2\alpha /\mathrm{d}{\phi }^2)(0)>0$. 对于联轴器$\alpha (\phi )=\mathrm{经验值}(-\beta {\phi }^2/{米}_{\mathrm{pl}}^2)$， 在哪里 $\beta (<0)$ 是耦合常数且 ${米}_{\mathrm{pl}}$是约化的普朗克质量，除了具有消失标量场的广义相对论解，即爱因斯坦-麦克斯韦模型中的解之外，还有一个带电星解的分支，其非平凡的ϕ轮廓接近于 0 向空间无穷大。作为比${\rho }_C/{\rho }_{米}$ 电荷密度之间 ${\rho }_C$ 和物质密度 ${\rho }_{米}$向其最大值增加，广义相对论中带电恒星的质量M趋向于由于库仑排斥力的增加而增加。在这种情况下，由-1 阶负β引起的非平凡分支的出现有效地降低了广泛范围的中心物质密度的库仑力，导致与一般相对论分支中的带电恒星相比质量和半径更小。我们的分析表明，恒星的自发标量化不仅可以由曲率不变量的耦合引起，还可以由爱因斯坦引力中的标量-规范耦合引起。