Painlevé–Gullstrand coordinates

Painlevé–Gullstrand coordinates write the Schwarzschild metric as

d s^{2} = - d t^{2} + (d r + \frac{2 M}{r} d t)^{2} + r^{2} d Ω^{2} .

The constant-

t

spatial slices are flat, and the coordinates remain regular at the Schwarzschild radius.

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- Orthonormal coframe in Painlevé–Gullstrand coordinates Painlevé–Gullstrand coordinates

Orthonormal coframe in Painlevé–Gullstrand coordinates

An orthonormal coframe is

e^{0} = d t, e^{1} = d r + \frac{2 M}{r} d t, e^{2} = r d θ, e^{3} = r sin θ d ϕ .

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