Long Lived Quasinormal Modes of Regular and Extreme Black Holes

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.