Scalarized charged black holes with scalar mass term

We study the scalarized charged black holes in the Einstein-Maxwell-Scalar (EMS) theory with scalar mass term. In this work, the scalar mass term is chosen to be $m^2_ϕ=α/β$, where $α$ is a coupling parameter and $β$ is a mass-like parameter. It turns out that any scalarized charged black holes are not allowed for the case of $β\le 4.4$ with $q=0.7(M=0.5,Q=0.35)$ because this case implies the stable Reissner-Nodström (RN) black holes. In the massless limit of $β\to \infty$, one recovers the case of the EMS theory. We note that the unstable RN black hole implies the appearance of scalarized charged black holes. The other unstable case of $β>4.4$ with $q=0.7$ allows us to obtain the $n=0,1,2,\cdots$ scalarized charged black holes for $α(β)\ge α_{\rm th}(β)$ where $α_{\rm th}(β)$ represents the threshold of instability for the RN black hole. Furthermore, it is shown that the $n=0$ black hole is stable against radial perturbations, while the $n=1$ black hole is unstable. This stability result is independent of the mass parameter $β$.

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