  The Kerr spacetime is perhaps the most astrophysically important of the
currently known exact solutions to the Einstein field equations. Whenever
spacetimes can be put in unit-lapse form it becomes possible to identify some
very straightforward timelike geodesics, (the "rain" geodesics), making the
physical interpretation of these spacetimes particularly clean and elegant. The
most well-known of these unit-lapse formulations is the Painleve-Gullstrand
form of the Schwarzschild spacetime, though there is also a Painleve-Gullstrand
form of the Lense-Thirring (slow rotation) spacetime. More radically there are
also two known unit-lapse forms of the Kerr spacetime -- the Doran and Natario
metrics -- though these are not precisely in Painleve-Gullstrand form. Herein
we shall seek to explicate the most general unit-lapse form of the Kerr
spacetime. While at one level this is "merely" a choice of coordinates, it is a
strategically and tactically useful choice of coordinates, thereby making the
technically challenging but astrophysically crucial Kerr spacetime somewhat
easier to deal with.
