Moore General Relativity — Workbook Solutions

Derive the geodesic equation for this metric.

Derive the equation of motion for a radial geodesic. moore general relativity workbook solutions

Using the conservation of energy, we can simplify this equation to Derive the geodesic equation for this metric

$$\frac{t_{\text{proper}}}{t_{\text{coordinate}}} = \sqrt{1 - \frac{2GM}{r}}$$ moore general relativity workbook solutions

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