$ds^2=-(1-\frac{2Mr-Q^2}{\rho^2})dt^2+\frac{\rho^2}{\Delta}dr^2+\rho^2d\theta^2$

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

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

where

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

and

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

$$M$$ 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:

$ds^2=-(1-\frac{2Mr}{\rho^2})dt^2+\frac{\rho^2}{\Delta}dr^2+\rho^2d\theta^2$

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

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