# Metric of spinning magnetically charged black hole

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?

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 $$\cos^2 \alpha = Q_e^2/Q^2$$.
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.
$$a^2 + q^2 +g^2 \leq M^2 .$$