Moore — General Relativity Workbook Solutions

$$ds^2 = -\left(1 - \frac{2GM}{r}\right) dt^2 + \left(1 - \frac{2GM}{r}\right)^{-1} dr^2 + r^2 d\Omega^2$$

Consider the Schwarzschild metric

For the given metric, the non-zero Christoffel symbols are moore general relativity workbook solutions

The equation of motion for a radial geodesic can be derived from the geodesic equation. After some algebra, we find $$ds^2 = -\left(1 - \frac{2GM}{r}\right) dt^2 + \left(1

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