Physically motivated ansatz for the Kerr spacetime

Understand

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.