Linear stability of charged warm holes

Charged black holes are known to suffer from an interior instability associated with the presence of the Cauchy horizon. Recently, a hairy charged black hole was proposed that avoids the formation of a Cauchy horizon. It is natural to question whether this instability might manifest in the exterior solution. In this paper, we have analyzed the stability of this black hole. Our results show that vector perturbations are stable, along with the scalar sector for $l=0$. We have also computed the corresponding quasinormal modes (QNMs) and quasibound states (QBSs). Among the six degrees of freedom identified, one exhibits a ghost-like behavior. However, this mode decouples from the other perturbations, rendering the associated instability irrelevant in the linear regime. Nonetheless, this feature could indicate a more significant issue in the nonlinear regime.
Comment: 14 pages, 8 figures