Conformal compactification of Kerr spacetime I'm looking for a book/paper where the conformal compactification of Kerr spacetime is calculated. I've seen plenty of reference for the Minkowski, but none (explicitly calculated) for Kerr.
Thank you.
PS: prior to writing this post, I was already referred to "Large scale structure of spacetime" by Hawking and Ellis, but there they only discuss the maximal extension of Kerr (and other solutions), not conformal compactification calculation.
EDIT on what I meant by "compactification for Minkowski": The Minkowski metric is
$ds^{2}=-dt^{2}+dr^{2}+r^{2}d\Omega^{2}$
where $-\infty<t<\infty$ and $0\leq r<\infty$. (We now want to get the coordinates with finite ranges)
First go to the double-null coordinates $u=t-r$ and $v=t+r$, and then change to $T=\arctan u+\arctan v$, $R=\arctan v-\arctan u$. We then obtain
$ds^{2}=\omega^{-2}(T,R)(-dT^{2}+dR^{2}+\sin^{2}Rd\Omega^{2})$
with $\omega(T,R)=2\cos U \cos V=\cos T+\cos R$.
Therefore, the original metric is related to the new one by (explicitly given) conformal transf. $\omega^{2}$ as
$d\tilde{s}^{2}=\omega^{2}(T,R)ds^{2}=-dT^{2}+dR^{2}+\sin^{2}R d\Omega^{2}$
where $R,T$ have the finite ranges $0\leq R<\pi$ and $R-\pi <T <\pi -R$.
 A: See Section 8 of Pretorius and Israel, "Quasi-spherical light cones of the Kerr geometry". http://arxiv.org/abs/gr-qc/9803080  The paper contains quite a bit more of course. But I want to point out that in the expression you find there, $R^2$ is fairly reasonable as a quantity in the usual (say, Boyer-Lindquist) coordinates. But the function $r_*$ is quite difficult to get a handle on.  
A: Although the focus of the original question was on conformal compactification, a necessary step along the way is an introduction of double-null coordinates that are regular on the horizons and bifurcation spheres of Kerr (where the standard Boyer-Lindquist coordinates become singular). An alternative set of such coordinates, which are obtained in a briefer and more elementary way than the classic Pretorius-Israel references cited in Willie's answer can be found in

Hayward, Sean A., Kerr black holes in horizon-generating form, Phys. Rev. Lett. 92, No. 19, Article ID191101, 4 p. (2004). [arXiv:gr-qc/0401111] ZBL1267.83059.

