When does a Geodesic Represent a Free-Falling Particle's Worldline?

[deadringer]

"Under what conditions does a geodesic represent a possible wordline for a particle in free fall, parametrized by proper time."

I can only think of one conditions - the fact that the metric ds squared is positive. Is this enough?

 

[Dick]

Possibly something like, "if acted on by no nongravitational forces". GR only absorbs gravitational forces into the metric. Though possibly that violates the condition of 'free fall'.

 

[Dick]

Nope. I think you are basically right to begin with. 'Free fall' should exclude nongravitational forces. But I think the condition that they might be looking for is that the particle is massive. Otherwise proper time=0 is quite acceptable.