Analysis of a nonlinear electromagnetic generalization of the Reissner-Nordstr\"om black hole

In this work, we investigate the gravitational signatures of a nonlinear electromagnetic extension of the Reissner-Nordstr\"om solution. We conduct an analysis of light propagation, focusing on the photon sphere, shadow formation, and geodesic trajectories in this spacetime. The constraints on the parameter $\xi$, which characterizes the nonlinear extension of the Reissner-Nordstr\"om black hole, are derived from observational data provided by the Event Horizon Telescope (EHT). The time delay effects are also considered. In the thermodynamic analysis, we examine the Hawking temperature, entropy, heat capacity, and the emission of Hawking radiation via the tunneling process. The remnant mass and evaporation time of the black hole at its final stage are estimated. In addition, we compute the quasinormal modes using the WKB approximation, taking into account the characteristic oscillations of the system under scalar, vector, and tensor perturbations. Additionally, the time-domain solution is analyzed for all these perturbations to examine their evolution over time.