Effect of a Geodesic
A geodesic is the path of zero force. Look at the change in momentum (effect) term of 
.
- Start with the change in momentum set equal to zero. Apply the chain rule to expand:
- Assume
.
Use the chain rule to expand
:
- Apply the definition of a covariant derivative of a contravariant vector
(normal derivative - change in the metric,
):
If any acceleration is seen without a force (
),
then the effect is entirely due to the curvature of spacetime (
).
Slide 36 is long.