资料:Kerr-Newman Metric 克尔-纽曼度规

| 2012年12月18日

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

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

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

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:

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

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

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

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