Entropy in the NUT-Kerr-Newman Black Holes in the Background of de Sitter Space-Time

We calculate the entropy of the fermion field in the NUT-Kerr-Newman black holes in the background of the de Sitter space-time by using the improved brick-wall method and the membrane model. Here the Euler characteristic of the black holes is over two. The results show that, as the cut-off is properly chosen, the entropy in the black hole satisfies the Bekenstein-Hawking area law.