How Gravitational Forces arise from Curvature

In the second set of supplementary notes — Gravity, Metrics and Coordinates — we introduced the idea that matter induces spacetime curvature, and we argued that this curvature is fully described by the metric. In the case of a static, spherically symmetric mass distribution, we presented the Einstein Field Equations whose solution gives the metric and therefore the geometry of spacetime. The current notes complete the other half of our introduction to general relativity by deriving the equations of motion of massive bodies falling freely in a gravitational field.