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Please help: A world line is given to us. It is known that it is a geodesic. The metric, however, is not known. Since we don't know the metric, it should not be possible to tell whether the geodesic is spacelike/timelike/null (Right?)

But since the geodesic is known (x,y,z,t), we can find out ∂x/∂t, ∂y/∂t, ∂z/∂t. That is, we can find out the speed of the object which will travel that geodesic. Depending on whether it is greater than, equal to or less than 'c' (light speed), we can say that the geodesic is spacelike, null or timelike. Thus, it seems we can tell this without knowing the metric. What is wrong with this?

Thank you!

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# Nature of Geodesic

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