Optical and Radiative Properties of Black Hole in f(R, T) Gravity Coupled to Nonlinear Electrodynamics

In this work, we investigate the optical, radiative, and dynamical properties of a recently obtained charged black hole solution in [Formula: see text] gravity coupled to nonlinear electrodynamics (NLED). By considering the modified gravity model [Formula: see text] together with a power-law nonlinear electromagnetic Lagrangian, we study an extended Reissner–Nordström–(A)dS-like black hole geometry and analyze the influence of the matter–geometry coupling parameter [Formula: see text], the nonlinear electromagnetic coupling [Formula: see text], and the nonlinearity index [Formula: see text] on the spacetime structure and observable black hole characteristics. Our analysis shows that the parameter [Formula: see text] significantly modifies the effective spacetime curvature, alters the horizon structure, and acts as a curvature-screening parameter that shifts the photon sphere outward, leading to an increase in the black hole shadow radius. We further demonstrate that the nonlinear electrodynamics parameters [Formula: see text] and [Formula: see text] introduce substantial corrections to the metric function, thereby affecting the weak gravitational deflection angle, plasma-induced lensing behavior and greybody factor bounds. In addition, we show that the presence of a dispersive plasma medium makes the gravitational lensing phenomenon frequency dependent, producing noticeable deviations from the vacuum case. The combined effects of modified gravity and nonlinear electrodynamics therefore lead to distinct optical and radiative signatures that can provide useful observational probes for testing strong-field gravitational physics using current and future astrophysical observations.