Moore General Relativity Workbook Solutions May 2026

Consider the Schwarzschild metric

$$\frac{d^2r}{d\lambda^2} = -\frac{GM}{r^2} + \frac{L^2}{r^3}$$ moore general relativity workbook solutions

After some calculations, we find that the geodesic equation becomes moore general relativity workbook solutions

$$\frac{d^2t}{d\lambda^2} = 0, \quad \frac{d^2x^i}{d\lambda^2} = 0$$ moore general relativity workbook solutions

Derive the geodesic equation for this metric.

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

which describes a straight line in flat spacetime.