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The following has been confusing my friends and I, I want to make sure I have this clear as it is fairly elementary. (note set c = 1)

Ed is falling radially into a black hole, the Schwarzschild metric is:

ds^{2}= (1-2μ/r) dt^{2}- (1- 2μ/r)^{-1}dr^{2}

his proper time is dτ^{2}= (1-2μ/r) dt^{2}- (1- 2μ/r)^{-1}dr^{2}

If Simon is stationary and is coincident with Ed at some radius then he measures the proper distances and times given by:

dr_{s}= (1 - 2μ/r)^{-1/2}* dr and dt_{s}= (1 - 2μ/r)^{1/2}dt

I think that's all right. But then is Simon's metric dt_{s}^{2}- dr_{s}^{2}≈ ds^{2}= (1-2μ/r) dt^{2}- (1- 2μ/r)^{-1}dr^{2}or are these really meant to be different bases?

Many thanks.

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# Radial motion in the Schwarzshild spacetime

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