Chemistry - 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:

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

$\frac{\Delta}{\rho^{2}}\equiv \frac{r^{2}-{2}{M}{r}+a^{2}+Q^{2}}{r^{2}+a^{2}\cos^{2}\theta}$

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

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

Source(s)

Kerr-Newman Black Hole

Categories: General relativity | Equations