Kerr-newman Metric

The Kerr-Newman metric is a solution of Einstein's field equations that describes the spacetime geometry around a charged (Q\neq0), rotating (J\neq0) black hole of mass m. The Kerr-Newman metric is: ds^{2}=-\frac{\Delta}{\rho^{2}}\left(dt-a\sin^{2}\theta d\phi\right)^{2}+\frac{\sin^{2}\theta}{\rho^{2}}\left\left(r^{2}+a^{2}\right)d\phi-adt\right^{2} +\frac{\rho^{2}}{\Delta}dr^{2}+\rho^{2}d\theta^{2} \rho^{2}\equiv r^{2}+a^{2}\cos^{2}\theta a\equiv\frac{J}{m}

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