Categories: General relativity | Equations

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:

$ds^{2}=-\frac{\Delta}{\rho^{2}}\left(dt-a\sin^{2}\theta d\phi\right)^{2}+\frac{\sin^{2}\theta}{\rho^{2}}\left[\left(r^{2}+a^{2}\right)d\phi-{a}dt\right]^{2} +\frac{\rho^{2}}{\Delta}dr^{2}+\rho^{2}d\theta^{2}$