  Complex quantum information tasks in a gravitational background require
multipartite entanglement for effective processing. Therefore, it is necessary
to investigate the properties of multipartite entanglement in a relativistic
setting. In this paper, we study genuine N-partite entanglement of massless
Dirac fields in the Schwarzschild-de Sitter (SdS) spacetime, characterized by
the presence of a black hole event horizon (BEH) and a cosmological event
horizon (CEH). We obtain the general analytical expression of genuine N-partite
entanglement shared by n observers near BEH and m (n+m = N) observers near CEH.
It is shown that genuine N-partite entanglement monotonically decreases with
the decrease of the mass of the black hole, suggesting that the Hawking effect
of the black hole destroys quantum entanglement. It is interesting to note that
genuine N-partite entanglement is a non-monotonic function of the cosmological
constant, meaning that the Hawking effect of the expanding universe can enhance
quantum entanglement. This result contrasts with multipartite entanglement in
single-event horizon spacetime, offering a new perspective on the Hawking
effect in multi-event horizon spacetime.
