Quantum characteristics near event horizons

We investigate quantum characteristics around Schwarzschild black hole, exploring various quantum resources and their interplay in curved space-time. Our analysis reveals intriguing behaviors of quantum coherence, global and genuine multipartite entanglement, first-order coherence, and mutual information in different scenarios. Initially, we consider three particles shared among Alice, Bob, and Charlie in a Minkowski space far from the event horizon, where these particles are correlated via Greenberger-Horne-Zeilinger-type correlation. While Alice's particle remains in Minkowski space, Bob and Charlie accelerate towards the event horizon, experiencing black hole evaporation and generating antiparticles correlated via the Hawking effect. We employ the Kruskal basis formulation to derive a pentapartite pure state shared among particles inside and outside the event horizon. Investigating different scenarios among particles both inside and outside the event horizon, we observe how quantum resources evolve and distribute among consideration of different particles with Hawking temperature and mode frequency. The trade-off relationship between first-order coherence and concurrence fill persists, indicating the intricate interplay between coherence and entanglement. Notably, the mutual information between external observers and particles inside the black hole becomes nonzero, deepening our understanding of quantum effects in curved space-time and shedding light on the quantum nature of the black hole. We believe that these findings will pave the way for future investigations into the fundamental quantum mechanical aspects of gravity under extreme environments.