Moore General Relativity Workbook Solutions May 2026

The equation of motion for a radial geodesic can be derived from the geodesic equation. After some algebra, we find

where $L$ is the conserved angular momentum. moore general relativity workbook solutions

$$\frac{d^2r}{d\lambda^2} = -\frac{GM}{r^2} \left(1 - \frac{2GM}{r}\right) \left(\frac{dt}{d\lambda}\right)^2 + \frac{GM}{r^2} \left(1 - \frac{2GM}{r}\right)^{-1} \left(\frac{dr}{d\lambda}\right)^2$$ The equation of motion for a radial geodesic

This factor describes the difference in time measured by the two clocks. moore general relativity workbook solutions

Using the conservation of energy, we can simplify this equation to

Derive the equation of motion for a radial geodesic.

After some calculations, we find that the geodesic equation becomes