Moore General Relativity Workbook Solutions Online

For the given metric, the non-zero Christoffel symbols are

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

$$\frac{d^2r}{d\lambda^2} = -\frac{GM}{r^2} \left(1 - \frac{2GM}{r}\right) \left(\frac{dt}{d\lambda}\right)^2 + \frac{GM}{r^2} \left(1 - \frac{2GM}{r}\right)^{-1} \left(\frac{dr}{d\lambda}\right)^2$$ For the given metric, the non-zero Christoffel symbols