Quantum gravity corrections and plasma-induced lensing of magnetically charged black holes

This work investigates the influence of quantum gravity corrections and plasma effects on a magnetically charged black hole derived from Einstein-Nonlinear Electrodynamics theory. The nonlinear electromagnetic field leads to a regular geometry that removes the curvature singularity and modifies the near-horizon structure. Using the semiclassical tunnelling approach for Dirac particles, we derived the Hawking temperature and confirmed its agreement with the standard surface gravity method. Quantum effects are examined by adopting the Generalized Uncertainty Principle, which adds a minimal length scale to the theory and changes the familiar thermodynamic relations of black holes. With this correction, the temperature, entropy, and heat capacity gain small but meaningful shifts, implying that the evaporation process might stop before the mass completely vanishes. To extend the analysis, an exponential term was introduced into the entropy expression, making it possible to explore how such contributions alter quantities like internal energy, free energy, and pressure. The results suggest that these quantum terms influence the stability of the system and can lead to transitions between different thermodynamic phases depending on the magnetic charge. The Joule-Thomson process was also studied to understand how the black hole cools or heats during an isenthalpic expansion. In the last part, the deflection of light was calculated in both vacuum and plasma surroundings using the Gauss-Bonnet theorem. It was observed that magnetic charge slightly weakens the bending, while plasma enhances it due to its refractive character. Taken together, the findings show how nonlinear electrodynamics, quantum corrections, and plasma dispersion jointly affect the behavior of magnetically charged black holes, linking microscopic corrections to their observable features.