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I am reading this paper about "Hawking radiation of Kerr-Newman-de Sitter black hole", where the authors find Hawking temperature of this metric

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The authors state that hawking temperature is given by

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The problem is I am not sure how enter image description here gives enter image description here. I have differentiated $\Delta_{r}$ with respect $r$ and did not get the same result. How did the author get the term on the RHS of equation $(8)$?

Thanks.

WhyME
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