Moore General Relativity Workbook Solutions May 2026
After some calculations, we find that the geodesic equation becomes
Derive the equation of motion for a radial geodesic. moore general relativity workbook solutions
where $\lambda$ is a parameter along the geodesic, and $\Gamma^\mu_{\alpha\beta}$ are the Christoffel symbols. After some calculations, we find that the geodesic
$$\frac{d^2r}{d\lambda^2} = -\frac{GM}{r^2} + \frac{L^2}{r^3}$$ After some calculations
$$\frac{t_{\text{proper}}}{t_{\text{coordinate}}} = \sqrt{1 - \frac{2GM}{r}}$$
