We discuss the tension between the possible existence of Painleve-Gullstrand
coordinate systems versus the explicit geometrical features of the Kerr
spacetime; a subject of interest to Professor Thanu Padmanabhan in the weeks
immediately preceding his unexpected death. We shall carefully distinguish
strong and weak Painleve-Gullstrand coordinate systems, and conformal variants
thereof, cataloguing what we know can and cannot be done — sometimes we can
make explicit global statements, sometimes we must resort to implicit local
statements. For the Kerr spacetime the best that seems to be achievable is to
set the lapse function to unity and represent the spatial slices with a
3-metric in factorized unimodular form; this arises from considering the Doran
version of Kerr spacetime in Cartesian coordinates. We finish by exploring the
(limited) extent to which this construction might possibly lead to implementing
an “analogue spacetime” model suitable for laboratory simulations of the Kerr
spacetime.
