Moore General Relativity Workbook: Solutions

After some calculations, we find that the geodesic equation becomes

Consider the Schwarzschild metric

which describes a straight line in flat spacetime. moore general relativity workbook solutions

$$ds^2 = -\left(1 - \frac{2GM}{r}\right) dt^2 + \left(1 - \frac{2GM}{r}\right)^{-1} dr^2 + r^2 d\Omega^2$$ After some calculations, we find that the geodesic

where $L$ is the conserved angular momentum. After some calculations