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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

enter image description here

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.

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  • $\begingroup$ I took a quick look at the paper. It seems that they are using equations 6-7 to manipulate the expression. In particular it seems that $M$ is replaced with the help of equation $7$. But maybe you are already aware of this. $\endgroup$
    – DelCrosB
    Commented Dec 20, 2016 at 11:19
  • $\begingroup$ @DelCrosB, I did notice that but I am still not sure how they got their result. $\endgroup$
    – WhyME
    Commented Dec 20, 2016 at 12:49
  • $\begingroup$ Is your question how the expression for $T_+$ is obtained in the first place (which would be a question about the physics of Hawking radiation) or solely how the r.h.s. of eq. (8) is obtained, which seems to just be a question about algebraic manipulations. $\endgroup$
    – ACuriousMind ♦
    Commented Dec 20, 2016 at 15:30

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