Shadow of a Nonlinear Electromagnetic Generalized Kerr–Newman–AdS Black Hole

In this work, we investigate the shadow properties of the Kerr–Newman–Anti-de Sitter black hole coupled to nonlinear electrodynamics. The shadow is constructed by employing the celestial coordinate approach for an observer located at a finite distance, which is required due to the non-asymptotically flat structure of the spacetime. The size, distortion, area, and oblateness of the shadow are analyzed in terms of the black hole parameters, namely, the spin, the effective charge, and the nonlinearity parameter. We show that the nonlinear electrodynamics significantly modifies the photon region and therefore changes the shadow observables, while the rotation mainly controls the deformation of the silhouette. We further confront the theoretical results with the Event Horizon Telescope observations of M87* and Sgr A* in order to constrain the parameter space of the model. The allowed ranges of the effective charge depend sensitively on the nonlinearity parameter, and the combination of both sources leads to tighter and physically more consistent bounds. In addition, we study the energy emission rate derived from the shadow radius and the Hawking temperature and discuss how it is affected by the rotation and the nonlinear electromagnetic field. Our analysis shows that the considered black hole solution provides a consistent extension of the Kerr geometry in a non-asymptotically flat background and that the shadow observables can be used as an efficient tool to test the effects of nonlinear electrodynamics in strong gravity.