# What coordinates are used to transform these metrics?

From reading different texts on kerr metric it seem that the kerr metric can be written in two different metrices Kerr metric

and Kerr metric

Does anyone know what coordinate change can be used to get the second metric from the first one?

• Would be nice with equation numbers, I didn't manage to find the second equation. – Emil Feb 2 '17 at 20:41

Boyer-Lindquist coordinates have been used for the first metric:

$$x = \sqrt{r^2 + \alpha^2}\sin\theta\cos\phi$$

$$y = \sqrt{r^2 + \alpha^2}\sin\theta\sin\phi$$

$$z = r\cos\theta$$

With

$$\alpha = \frac{J}{Mc}$$

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

$$\Delta = r^2 + r_2^2r + \alpha^2$$

$$r_s = \frac{2GM}{c^2}$$