Weakly magnetized black holes in Einstein-ModMax theory

We investigate magnetized black holes within the framework of Einstein gravity coupled to modified Maxwell (ModMax) nonlinear electrodynamics. Employing Wald's magnetization method, we construct a weakly magnetized static dyonic black hole solution ensuring that both electric and magnetic charges contribute nontrivially to the dynamics. The presence of the ModMax parameter v introduces a screening effect that effectively reduces the black hole's charge compared to the standard Maxwell case. We analyze the motion of charged timelike test particles in this magnetized background by deriving the effective potential and studying the characteristics of stable circular orbits, including the dependence of the innermost stable circular orbit (ISCO) on the magnetic field strength and the nonlinear parameter. Our results highlight differences between the dynamics in Einstein-ModMax theory and those in the conventional Einstein-Maxwell framework, offering new insights into the phenomenology of nonlinear electrodynamics in strong gravitational fields.