physics - Kerr-Newman

The Kerr-Newman metric is a solution to the equations of Einstein's general relativity theory. This metric is valid for the exterior of a charged ( $Q\neq0$ ), rotating ( $J\neq0$ ) black hole of mass $m$ .

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

$\Delta\equiv r^{2}-2mr+a^{2}+Q^{2}$

$\rho^{2}\equiv r^{2}+a^{2}\cos^{2}\theta$

$a\equiv\frac{J}{m}$

External links

Kerr-Newman Black Hole

Categories: General relativity