Spontaneous scalarization of Bardeen black holes

Abstract: We study the spontaneous scalarization of Bardeen black holes, whose tachyonic instability triggers the formation of scalarized charged black holes (SCBHs). In this case, we find infinite ($n=0,1,2,\cdots$) branches of SCBHs with magnetic charge $g$. The $n = 0$ branch of SCBHs can be found for the coupling parameter $\alpha \geq \alpha_{n=0}(g)$ with both quadratic (1-$\alpha \varphi^2$) and exponential ($e^{-\alpha \varphi^2}$) couplings, where $\alpha_{n=0}(g)$ represents the threshold of tachyonic instability for the Bardeen black holes. Furthermore, it is shown that the $n = 0$ branch for both couplings is stable against radial perturbations. This stability shows that this branch can be used for further observational implications.