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is it true that for any valid spacetime in general relativity that:

if time dilated/contracted by k, space is contracted/dilated by k?

what is the mathematical explanation for this?

therefore, if one knows the time dilation for a point in spacetime, then one knows automatically the length contraction?

for the Kerr metric, the problem is that at the event horizon of a black hole space is infinitely contracted but time does not seem infinitely dilated...

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# Conservation of the volume form

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