\[ds^2=-(1-\frac{2Mr-Q^2}{\rho^2})dt^2+\frac{\rho^2}{\Delta}dr^2+\rho^2d\theta^2\]
\[+[(r^2+a^2)\sin^2\theta +\frac{(2Mr-Q^2)a^2\sin^4\theta}{\rho^2}]d\phi^2\]
\[- \frac{ 2(2Mr-Q^2)a\sin^2\theta}{\rho^2} dtd\phi\]
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:
\[ds^2=-(1-\frac{2Mr}{\rho^2})dt^2+\frac{\rho^2}{\Delta}dr^2+\rho^2d\theta^2\]
\[+[(r^2+a^2)\sin^2\theta +\frac{2Mra^2\sin^4\theta}{\rho^2}]d\phi^2\]
\[- \frac{ 4Mra\sin^2\theta}{\rho^2} dtd\phi\]
