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## Main Question or Discussion Point

(This could be a dumb question, but in any case I'll be happy if the answer is simple)

I understood that the path of a freely moving object in space satisfies the geodesic equation, but I'm not fully sure how precisely to deal with the four momentum of the object. Have I understood this correctly, if I think that the four momentum is a tangent vector to the path, and that the time evolution of the four momentum is obtained by parallel transport along the path?

I understood that the path of a freely moving object in space satisfies the geodesic equation, but I'm not fully sure how precisely to deal with the four momentum of the object. Have I understood this correctly, if I think that the four momentum is a tangent vector to the path, and that the time evolution of the four momentum is obtained by parallel transport along the path?