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According to Wikipedia (as of 1/20/2021), black holes may be completely classified according to their mass, electric charge and angular momentum. Are there not also 'magnetic monopole' solutions to Einstein's equations for black holes that enclose a net magnetic charge? If not, why might that be? If so, are the physical bounds or limiting cases of 'magnetic' black holes comparable to those of the Kerr and Kerr-Newman varieties?

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One could easily check that the stress–energy–momentum tensor of Maxwell field is invariant under electric–magnetic duality transformation. Therefore the metric of Kerr–Newman black hole carrying only electric charge $Q$ is also the metric of dyonic black hole carrying both electric $Q_e$ and magnetic $Q_m$ charges under replacement $Q^2\to Q_e^2 + Q_m^2$. Maxwell tensor $F$ is obtained by “rotation” of pair $(F,\tilde{F})$ by an angle $\alpha$, such that $\cos^2 \alpha = Q_e^2/Q^2$.

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The general metric for a black hole with electric charge $q$ and magnetic charge $g$ is obtained by replacing $q^2$ in the standard Kerr-Newman solution by $q^2+g^2$. The result is usually also called the "Kerr-Newman" solution.

In particular, the necessary condition for the singularity to be covered by a horizon is simply

$$ a^2 + q^2 +g^2 \leq M^2 .$$

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