Nonlinear electrodynamic black holes and their role in testing modified theories of gravity

The nature of black holes (BHs) and their potential deviations from classical General Relativity (GR) remain central questions in modern astrophysics. Nonlinear electrodynamics (NED) offers a promising mechanism to construct regular BHs that avoid singularities while retaining key astrophysical features. In this work, we analyze NED-inspired BHs and derive constraints on the magnetic parameter using Bayesian parameter estimation from Event Horizon Telescope (EHT) observations. We obtain $q = 0.63 ^{+0.68}_{-0.44} \times 10^9 M_{\odot}$ for M87* and $q = 0.33 ^{+0.36}_{-0.23} \times 10^6 M_{\odot}$ for Sgr A*, affecting their horizon structure. A comparison with the Schwarzschild solution highlights deviations in geometry and horizon properties, emphasizing the impact of NED. We also examine observational signatures, including BH shadows and gravitational lensing. Using $R_{\text{sh}} = r_{\text{ph}} \sqrt{1/f(r_{\text{ph}})}$, we explore shadow features under uniform and non-uniform plasma conditions, revealing deviations from GR predictions due to NED effects. By analyzing photon sphere shifts and lensing patterns, we identify observable features that distinguish these BHs from classical ones. Our results suggest that NED-induced modifications may leave detectable imprints in strong-field regimes, opening pathways to test alternative gravity models. Future missions such as the Laser Interferometer Space Antenna (LISA) and next-generation X-ray observatories, along with ongoing observations from the EHT and gravitational wave detections by the Laser Interferometer Gravitational-Wave Observatory and Virgo (LIGO--Virgo), will be essential for refining constraints on such models.