# $g^{\mu \nu}$ (inverse metric) for Kerr metric in ingoing Kerr coordinates

I need to do a calculation in ingoing Kerr coordinates. I have $g_{\mu\nu}$ from which $g^{\mu\nu}$ can be obtained by hand. However there are so many terms and the final result is not in good form. So is there any reference where $g^{\mu\nu}$ is given ?

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• Landau Vol.2 6th edition, expression 104.6 gives the inverse Kerr metric. – DelCrosB Oct 14 '16 at 10:06
• But it is in Boyer-Lindquist coordinates. I am looking for the inverse metric in $\textit{Ingoing Kerr coordinates}$. – Prof Shonku Oct 14 '16 at 10:14