I had this doubt studing GR, but lets consider SR for semplicity,(adsbygoogle = window.adsbygoogle || []).push({});

where [itex]g_{\mu\nu}=\eta_{\mu\nu}[/itex]the geodesics are

[itex]0=ds^2=dt^2-dr^2[/itex]

we obtain the constraint we obtain the constraint r=(+/-)t

So it is a well known light cone, but in SR we have that a (test?)particle can always move in a line described by r=vt with v<c

Where this come from? seems to me that geodesics are just light cone and not trajectories allowed by common test particles.

In particular, given the metric tensor and the initial conditions of a particle(speed and position) how can be derived the line he follows?

I know there questions are trivial, but for a new player as me, GR seems very subtle and elusive.

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# If Geodesic are light cone, how can be test particle trajectiories

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