# In what coordinates is the following Kerr metric writing in?

In this book the kerr metric was given by

I am confused because of the appearance of the $2d\nu dr$ term because in the standard Kerr metric I know this term doesn't appear. Does anyone know what coordinates is this metric given by and the relationship between these coordinates and the standard Kerr coordinates?

Thanks.

"The coordinates $(\nu,r,\theta,\bar \phi)$ are the Kerr coordinates."
The section 19.4.1 in your reference discusses in detail how to get from Boyer-Lindquist coordinates to this so called Kerr coordinates. The term you are confused about come from the $-dt^2$ and the $dr^2$ terms in Boyer-Lindquist coordinates, using the coordinate change $d\nu=dt +\frac{r^2+a^2}{\Delta}dr$, which is described in eq. (19.42).
• Do you mean that if I change coordinate by $d\nu=dt +\frac{r^2+a^2}{\Delta}dr$ then the metric I gave changes to the metric in Wikipedia? – gbd Sep 14 '16 at 22:58
• If they both use the same coordinates then why does the $2d\nu dr$ term only appears in one of them? – gbd Sep 14 '16 at 23:02
• You can write the line element $ds^2$ in Boyer-Lindquist coordinates $(t,r,\theta,\phi)$ or in Kerr coordinates $(\nu,r,\theta,\bar\phi)$. The line element in those two coordinates looks differently and you can get from one to another using the coordinate changes. – M. J. Steil Sep 14 '16 at 23:04