  Despite some 60 years of work on the subject of the Kerr rotating black hole
there is as yet no widely accepted physically based and pedagogically viable
ansatz suitable for deriving the Kerr solution without significant
computational effort. (Typically involving computer-aided symbolic algebra.)
Perhaps the closest one gets in this regard is the Newman-Janis trick; a trick
which requires several physically unmotivated choices in order to work. Herein
we shall try to make some progress on this issue by using a non-ortho-normal
tetrad based on oblate spheroidal coordinates to absorb as much of the messy
angular dependence as possible, leaving one to deal with a relatively simple
angle-independent tetrad-component metric. That is, we shall write $g_{ab} =
g_{AB} \; e^A{}_a\; e^B{}_b$ seeking to keep both the tetrad-component metric
$g_{AB}$ and the non-ortho-normal co-tetrad $e^A{}_a$ relatively simple but
non-trivial. We shall see that it is possible to put all the mass dependence
into $g_{AB}$, while the non-ortho-normal co-tetrad $e^A{}_a$ can be chosen to
be a mass-independent representation of flat Minkowski space in oblate
spheroidal coordinates: $(g_\mathrm{Minkowski})_{ab} = \eta_{AB} \; e^A{}_a\;
e^B{}_b$. This procedure separates out, to the greatest extent possible, the
mass dependence from the rotational dependence, and makes the Kerr solution
perhaps a little less mysterious.
