  We investigate the genuine multipartite entanglement, global entanglement,
and quantum coherence among different configurations of a penta-partite system
involving particles inside and outside the event horizon of a Schwarzschild
black hole. We consider and analyze different scenarios based on how many
particles are accessible. In each scenario, we evaluate first-order coherence,
concurrence fill, and global concurrence under varying Hawking temperature and
Dirac particle mode frequency. For the fully accessible scenario with all
particles outside the event horizon, the measures exhibit non-monotonic
behavior with a discernible trade-off. In the partially accessible scenarios
with one particle inside the event horizon, monotonic variations and clear
trade-offs are observed. Finally, in the scenario when two particles are inside
the event horizon, concurrence fill becomes complex, attributed to the
violation of the entanglement polygon inequality in curved space-time. This
result reveals intricate relationships between entanglement and coherence
around the event horizon of Schwarzchild black holes. Our findings suggest
reevaluating entanglement polygon inequalities and concurrence fill for
applicability in flat and curved space-times. These insights contribute to our
understanding of quantum information dynamics and gravitational impacts on
entanglement in extreme environments.
