ModMax Black Holes in 4-Dimensional Einstein-Gauss-Bonnet Gravity

Abstract: In this paper, we study charged black hole solutions in 4-dimensional Einstein-Gauss-Bonnet gravity combined with ModMax nonlinear electrodynamics. This is a conformally invariant extension of Maxwell theory that effectively describes nonlinear electromagnetic phenomena. Within the regularized 4-dimensional Gauss-Bonnet framework, we derive an exact static and spherically symmetric black hole solution that is sourced by a purely electric ModMax field. We explore how higher curvature corrections and nonlinear electromagnetic effects change the spacetime geometry, horizon structure, and energy content of the black hole. We examine the thermodynamic properties in detail, revealing a minimum mass and stable black hole remnants. These findings might be significant in scenarios involving dark-sector compact objects or evaporation endpoints beyond standard general relativity. We also investigate the motion of massive particles, discussing the characteristics of circular orbits and the innermost stable circular orbit, highlighting differences from the Maxwell case. Additionally, we analyze the quasinormal modes of a massive scalar field using WKB methods with Padé approximants and the Pöschl-Teller approximation. We explore how the quasinormal spectrum depends on the Gauss-Bonnet coupling, the ModMax parameter, and the scalar field mass. Our results confirm the linear stability of the black hole and offer potential observational signatures of dark-sector inspired modifications of gravity and electrodynamics.