Separable geodesic action slicing in stationary spacetimes

Abstract

A simple observation about the action for geodesics in a stationary spacetime with separable geodesic equations leads to a natural class of slicings of that spacetime whose orthogonal geodesic trajectories represent freely falling observers. The time coordinate function can then be taken to be the observer proper time, leading to a unit lapse function. This explains some of the properties of the original Painlevé-Gullstrand coordinates on the Schwarzschild spacetime and their generalization to the Kerr-Newman family of spacetimes, reproducible also locally for the Gödel spacetime. For the static spherically symmetric case the slicing can be chosen to be intrinsically flat with spherically symmetric geodesic observers, leaving all the gravitational field information in the shift vector field.

17 pages, 1 figure; published version

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Cited by in corpus (7)

• Coordinate families for the Schwarzschild geometry based on radial timelike geodesics
• Black hole geodesic parallel transport and the Marck recipe for isolating cumulative precession effects
• Schwarzschild spacetime under generalised Gullstrand-Painlevé slicing
• Godel spacetime: elliptic-like geodesics and gyroscope precession
• On the meaning of Painlevé--Gullstrand synchronization
• Slicing black hole spacetimes
• Relative-observer definition of the Simon tensor