Superradiant (In)stability, Greybody Radiation, and Quasinormal Modes of Rotating Black Holes in Non-Linear Maxwell f(R) Gravity

This work is dedicated to the investigation of superradiant stability a rotating black hole derived from nonlinear Maxwell theory gravity, f(R). The evaluation and instability in this study will be based on absence presence magnetic field, respectively, when field constant c4=0 c4≠0. For under discussion, analyses greybody factors (GFs) quasi-normal modes (QNMs) are also carried out. To end, we first consider Klein–Gordon equation for scalar waves propagating hole’s geometry. resulting radial then reduced one-dimensional Schrödinger-like wave with effective potential energy. effects f(R) gravity parameters (q, c, c4) potential, GFs, QNMs examined. results demonstrate that, although q, c4 all influence they do not affect GFs QNMs. All presented summarized using appropriate graphics tables.