differential geometry

Blah. Covariant derivative. Parallel transport. What's the story?

"a geodesic is a curve whose parametrization, when viewed from within the surface, appears to have zero acceleration" (i.e., all of the acceleration is normal to the surface)

The phrase "objects not experiencing external forces follow geodesics" is more of a tautology than I thought.

If gravity is actually a warping of space-time — so that there's not actually any 'force' of gravity, but rather falling objects travel in "straight lines" along geodesics in space time — why is there still the occasional mention of graviton messenger particles for the gravitational force?

sleepy time.