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Radial perturbations of the scalarized black holes in Einstein-Maxwell-conformally coupled scalar theory

We perform the stability analysis for the scalarized charged black holes obtained from Einstein-Maxwell-conformally coupled scalar (EMCS) theory by employing the radial perturbations. The targeting black holes include a single branch of scalarized charged black hole with the coupling parameter $α>0$ inspired by the constant scalar hairy black hole as well as infinite branches of $n=0(α\ge 8.019),1(α\ge 40.84),2(α\ge 99.89),\cdots$ scalarized charged black holes found through the spontaneous scalarization on the Reissner-Nordström black hole. It turns out that the black hole in the single branch and the $n = 0$ black hole are stable against radial perturbations, while the $n = 1, 2$ excited black holes are unstable in the EMCS theory with both quadratic and exponential couplings.