Negative potential-induced scalarization in the Einstein-Euler-Heisenberg black hole*

Abstract We investigate a negative potential-induced scalarization of the Einstein-Euler-Heisenberg (EEH) black hole in the EEH-scalar theory, characterized by mass M , Euler-Heisenberg parameter μ , and magnetic charge q . In the regime (with ), the black hole admits a single horizon and allows for overcharged configurations with . We obtain a single branch of scalarized EEH (sEEH) black holes for , which is considered as the simplest model for scalarization of EEH black holes. We find that this class of hairy black holes is not thermodynamically favored, and their quasinormal modes indicate that they are dynamically unstable. A notable feature is that the scalar charge depends weakly on q for but grows more rapidly for , suggesting a transition from primary- to secondary-type scalar charge. This finding reveals characteristic properties of hairy black holes in EEH theory, specifically in the overcharging regime.