Re-parametrization of Geodesics: Can You Confirm?

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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=fVfor the geodesic equation?
 
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bloby said:
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=fVfor the geodesic equation?

Yes. Only parameters related by a linear function will satisfy the simple form of geodesic equation. Further, invariant interval (proper time or distance) is one of the possible solutions, so only e.g. aτ+b will work as another parametrization and still satisfy this equation.
 
Ok, thank you.
 
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