In this paper, by considering energy conservation and the self-gravitation reaction in the dynamical background space-time, we attempt to extend Kerner and Mann's work to the Vaidya-de Sitter black hole by the fermion-tunneling method. The result we derive shows that the tunneling probability of the Vaidya-de Sitter black hole is related not only to the change in the Bekenstein-Hawking entropy but also to the integral of the changing horizon, which are different from the stationary cases.
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