Quantum Entanglement in the Dirac Field Quantization around Charged Black Holes

We investigate the quantum entanglement properties of the Dirac field near a charged Reissner--Nordstr\"om black hole, incorporating the effects of Hawking radiation within the framework of quantum field theory in curved spacetime. Using concurrence $C$ and Bures distance $B$ as measures of entanglement, we analyze how quantum correlations evolve with respect to the electric charge $Q$ of the black hole, the frequency $\omega$ of fermionic modes, and the initial entanglement angle $\theta$. Our results show that the electric charge $Q$ enhances decoherence inside the event horizon while, counterintuitively, temporarily increasing accessible entanglement outside. The Hawking effect induces an apparent loss of entanglement for an external observer, due to correlation transfer to inaccessible regions. High-frequency modes $\omega$ exhibit greater resilience to gravitational effects, maintaining robust correlations near the horizon. These findings highlight the redistribution of entanglement in a multipartite system in curved spacetime, with significant implications for quantum information in relativistic and gravitational contexts.