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I hope this is not just an algebra mistake (and I'm very sorry if it is). Also, note I use the convention that the time argument is negative.

Setting $G=M=c=1$ for the Schwarzschild metric, it becomes $$g_{\mu \nu} = \left(\begin{matrix}-\left(1-2/r \right)&0&0&0\\0&\left(1-2/r \right)^{-1}&0&0\\0&0&r^2&0\\0&0&0&r^2\sin^2\theta \end{matrix}\right)$$

But, when I set $G=M=c=\epsilon_0=1$ and $Q=L=0$ in the Kerr-Newman metric (from Wikipedia), I get $$g_{\mu \nu} = \left(\begin{matrix}-\left(1-2/r \right)&0&0&0\\0&\left(r-2 \right)^{-2}&0&0\\0&0&r^2&0\\0&0&0&r^2\sin^2\theta \end{matrix}\right)$$

It seems to me that this metric should reduce to the Schwarzschild metric when there is no angular momentum or net charge. Can someone tell me why this isn't the case?

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Setting $J = 0$, $Q = 0$ in the metric of Kerr-Newman spacetime expressed in Boyer-Lindquist coordinates gives you Schwarschild metric in Schwarzschild coordinates. I don't see how you arrived at the metric you propose.

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  • $\begingroup$ Agreed, looks like some sort of algebra error. You are only off by a single factor of r on the second term. $\endgroup$ May 15, 2017 at 23:45

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