I imagine a point-like particle can only experience the local properties of spacetime. But locally there is no curvature and no gravity, as it is often stated that
Locally, as expressed in the equivalence principle, spacetime is Minkowskian, and the laws of physics exhibit local Lorentz invariance.(Wikipedia:General relativity)
But if this is the case how does a point-like particle know, which direction it should follow in a gravitational field?
Can this be a seen as a hint that point-like particles cannot be used as underlying concept for a field theory like general relativity?