We extend the classical Damour-Ruffini method and discuss Hawking radiation in Schwarzschild -de Sitter black hole. Under the condition that the total energy of spacetime is conservative, considering the effect of radiation particle on the spacetime and the relevance between the black hole event horizon and cosmological horizon, we obtain the black hole radiation spectrum. The radiation spectrum is no longer a pure thermal spectrum. It is related to Bekenstein-Hawking entropy change corresponding to the black hole event horizon and cosmological horizon. The result is consistent with an underlying unitary theory.
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