Gravitational signatures of a nonlinear electrodynamics in <i>f</i>(<i>R</i>,<i>T</i>) gravity

Abstract In this work, we investigate a nonlinear electrodynamics model in the context of f ( R , T ) gravity. We begin by outlining the general features of the theory and analyzing the event horizon under conditions ensuring its real and positive definiteness. We then examine light trajectories, focusing on critical orbits, shadow radii, and geodesics of massless particles. The parameters α and β , associated with the nonlinear extension of the Reissner-Nordström spacetime, are constrained using observational data from the Event Horizon Telescope (EHT). Subsequently, we analyze the thermal aspects of the system, including Hawking temperature, entropy, and heat capacity. Quasinormal modes are computed for scalar, vector, tensor, and spinorial perturbations, with the corresponding time-domain profiles explored as well. Gravitational lensing is then studied in both weak and strong deflection limits, along with the stability of photon spheres. Finally, we examine additional topological aspects, including topological thermodynamics and the topological photon sphere.