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Suppose you have a sphere, travelling at [itex]u = 0.99 c [/itex] along the [itex]x[/itex] axis in our frame S.

I was wondering how the sphere's metric changes due to Lorentz length contraction. Obviously at the rest frame of the sphere, it will appear as a sphere. However on S the sphere will appear as an ellipsoid.

How would the induced metric transform however, so that it changes from describing a sphere to describing an ellipsoid?

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# Sphere-Ellipsoid induced metrics

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