After some calculations, we find that the geodesic equation becomes
The equation of motion for a radial geodesic can be derived from the geodesic equation. After some algebra, we find moore general relativity workbook solutions
$$ds^2 = -dt^2 + dx^2 + dy^2 + dz^2$$
which describes a straight line in flat spacetime. After some calculations, we find that the geodesic
Using the conservation of energy, we can simplify this equation to After some calculations
where $\lambda$ is a parameter along the geodesic, and $\Gamma^\mu_{\alpha\beta}$ are the Christoffel symbols.