Stability of scalarized charged black holes in the Einstein-Maxwell-Scalar theory

Understand

We analyze the stability of scalarized charged black holes in the Einstein-Maxwell-Scalar (EMS) theory with quadratic coupling.

• These black holes are labelled by the number of $n=0,1,2,\cdots$, where $n=0$ is called the fundamental black hole and $n=1,2,\cdots$ denote the $n$-excited black holes.
• We show that the $n=0$ black hole is stable against full perturbations, whereas the $n=1,2$ excited black holes are unstable against the $s(l=0)$-mode scalar perturbation.
• This is consistent with the EMS theory with exponential coupling, but it contrasts to the $n=0$ scalarized black hole in the Einstein-Gauss-Bonnet-Scalar theory with quadratic coupling.