## re-parametrization of geodesics

Hello.

If I find a solution of the geodesic equation and I change the parametrization, the new function does not
satisfy this equation for a general re-parametrization. But the world line is the same.

Can you confirm it: does it come from the fact that we usually choose $\nabla_VV=0$ instead of
$\nabla_VV=fV$for the geodesic equation?

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 Quote by bloby Hello. If I find a solution of the geodesic equation and I change the parametrization, the new function does not satisfy this equation for a general re-parametrization. But the world line is the same. Can you confirm it: does it come from the fact that we usually choose $\nabla_VV=0$ instead of $\nabla_VV=fV$for the geodesic equation?