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Kerr–Newman metric:

[tex]c^{2} d\tau^{2} = - \left(\frac{dr^2}{\Delta} + d\theta^2 \right) \rho^2 + (c \; dt - \alpha \sin^2 \theta \; d\phi)^2 \frac{\Delta}{\rho^2} - ((r^2 + \alpha^2) d\phi - \alpha c \; dt)^2 \frac{\sin^2 \theta}{\rho^2}[/tex]

I used the Kerr–Newman metric equation form listed on Wikipedia for the purpose of isolating the Einstein tensor metric element functions for this particular metric. I expanded all the terms, combined all similar terms, then factored all the terms, and the result was this solution:

[tex]c^{2} d\tau^{2} = \frac{(\Delta - \alpha^2 \sin^2 \theta)}{\rho^2} \; c^2 \; dt^2 - \left(\frac{\rho^2}{\Delta} \right) dr^2 - \rho^2 d\theta^2 + (\alpha^2 \Delta \sin^2 \theta - r^4 - 2 r^2 \alpha^2 - \alpha^4) \frac{\sin^2 \theta \; d\phi^2}{\rho^2} - (\Delta - r^2 - \alpha^2) \frac{2 \alpha \sin^2 \theta \; c \; dt \; d\phi}{\rho^2}[/tex]

Is there anyone here qualified to verify this solution?

Reference:

Kerr-Newman metric - Wikipedia

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# Kerr–Newman metric

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