Painleve-Gullstrand form of the Lense-Thirring spacetime

Understand

The standard Lense-Thirring metric is a century-old slow-rotation large-distance approximation to the gravitational field outside a rotating massive body, depending only on the total mass and angular momentum of the source.

• Although it is not an exact solution to the vacuum Einstein equations, asymptotically the Lense-Thirring metric approaches the Kerr metric at large distances.
• Herein we shall discuss a specific variant of the standard Lense-Thirring metric, carefully chosen for simplicity, clarity, and various forms of "improved" behaviour, (to be more carefully defined in the body of the article).
• In particular we shall construct an explicit unit-lapse Painleve-Gullstrand variant of the Lense-Thirring spacetime, that has flat spatial slices, a very simple and physically intuitive tetrad, and extremely simple curvature tensors.