re-parametrization of geodesics

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 [itex]\nabla_VV=0[/itex] instead of
[itex]\nabla_VV=fV[/itex]for the geodesic equation?

PAllen

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.

bloby

Ok, thank you.