I'm by no means even adequate in the field of General relativity, so if my question is dumb, please excuse me.(adsbygoogle = window.adsbygoogle || []).push({});

Anyways, so I know that from the EFE's you can get the metric for the space-time you are considering, and from this metric you can get the geodesics of this space-time using calculus of variations. (Intensely tedious imo)

So, according to the GR, a freely moving body will move along to the geodesics, correct?

So, my question is, where does the velocity of that object come into play? I know that objects moving at different velocities will exhibit different trajectories, but this is not readily apparent if you just say all freely moving bodies will move along the geodesics of the space-time.

My guess on this matter would be that motion creates a Lorentz contraction (from Special relativity), which changes the space-time that you "see" in such a way that the geodesics are changed. Am I on the right track here? Or is there like a velocity term in the deriving of the geodesics, but it just doesn't look that way from the equations I've been looking at?

The equations for geodesics I'm looking at are (for the Schwarzchild metric):

[tex]\frac{d^2u}{d\phi^2}+u=\frac{m}{h^2}+3mu^2[/tex]

[tex]r^2\frac{d\phi}{ds}=h[/tex]

Where u=1/r, m and h are constants of integration (m is actually the mass of the sun). I was not told, in my textbook, what h actually is. Is h velocity dependent maybe?

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# Conceptual GR question (regarding orbit paths)

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