Null geodesics and null curves

blueelectrons
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What is the exact difference between null geodesics and null curves? Please explain both qualitatively and quantitatively.
 
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Null geodesics are parametrised such that the tangent vector is parallel transported along it. This is not necessarily the case for any null curve.
 
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Consider the path, in polar coordinates: θ = ct/R

A circular light speed path of radius R. This is null path that is not geodesic. Light would not take such a path in vaccuo.
 
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ok..thanks Orodruin and PAllen.
 
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