  The genuine entanglement of Dirac fields for an N-partite system is
investigated in Schwarzschild spacetime and the analysis is carried out using
the single-mode approximation. Due to the Hawking effect, quantum entanglement
is divided into two parts physically accessible and inaccessible entanglement.
We obtain a general analytic expression of genuine N-partite entanglement that
includes all accessible and inaccessible entanglement in a Schwarzschild black
hole. Unlike bosonic entanglement, the accessible N-partite entanglement of
Dirac fields monotonically decreases to a nonzero value with the Hawking
temperature. Interestingly, the inaccessible N-partite entanglement is a
monotonic or non-monotonic function of the Hawking temperature, depending on
the ratio between accessible and inaccessible modes, in contrast to bipartite
or tripartite entanglement that is only a monotonic function of the Hawking
temperature. Finally, we obtain two restrictive relationships for the quantum
information of the black hole. This conclusion provides a new understanding of
Hawking effect of the black hole.
