资料：Kerr-Newman Metric 克尔-纽曼度规

$$d{s}^2=-(1-\frac{2Mr-Q^2}{{\rho }^2})d{t}^2+\frac{{\rho }^2}{\mathrm{\Delta }}d{r}^2+{\rho }^{2}d{\theta }^2$$

$$+[(r^2+a^2){\sin }^2\theta +\frac{(2Mr-Q^2)a^2{\sin }^4\theta }{{\rho }^2}]d{\varphi }^2$$

$$-\frac{2(2Mr-Q^2)a{\sin }^2\theta }{{\rho }^2}dtd\varphi$$

where

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

and

$\mathrm{\Delta }=r^2-2Mr+a^2+Q^2$,

$M$ is the mass of the star,

$J$ is the whole,

$Q$ is the whole charge of the star.

If $Q=0$, we get Kerr metric:

$$d{s}^2=-(1-\frac{2Mr}{{\rho }^2})d{t}^2+\frac{{\rho }^2}{\mathrm{\Delta }}d{r}^2+{\rho }^{2}d{\theta }^2$$

$$+[(r^2+a^2){\sin }^2\theta +\frac{2Mr{a}^2{\sin }^4\theta }{{\rho }^2}]d{\varphi }^2$$

$$-\frac{4Mra{\sin }^2\theta }{{\rho }^2}dtd\varphi$$