Unit-lapse versions of the Kerr spacetime

Understand

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.