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 the superradiant stability of a rotating black hole derived from the nonlinear Maxwell theory of gravity, f (R). The evaluation of stability and instability in this study will be based on the absence and presence of the magnetic field, respectively, when the magnetic field constant is c(4 )? 0 and c4 =6 0. For the black hole under discussion, analyses of the greybody factors (GFs) and quasi-normal modes (QNMs) are also carried out. To this end, we first consider the Klein-Gordon equation for the scalar waves propagating in the black hole's geometry. The resulting radial equation is then reduced to a one-dimensional Schrodinger-like wave equation with effective potential energy. The effects of the nonlinear Maxwell f (R) gravity theory parameters (q, c, and c(4)) on the effective potential, GFs, and QNMs are examined. The results demonstrate that, although the parameters q, c, and c(4) all influence the effective potential, they do not affect the GFs and QNMs. All results are presented and summarized using appropriate graphics and tables.