Long-lived quasinormal modes of regular and extreme black holes

Abstract Recently, black-hole models in a nonlinear modification of the Maxwell electrodynamics were suggested, possessing simultaneously properties of an extreme charge and regularity ( Bronnikov K. A. , Phys. Rev. D , 110 (2024) 024021). We study quasinormal modes of a massive scalar field around such black holes and show that they are characterized by a comparatively small damping rate, indicating the possible existence of arbitrarily long-lived quasinormal modes, called quasi-resonances .