After some calculations, we find that the geodesic equation becomes
$$\frac{d^2t}{d\lambda^2} = 0, \quad \frac{d^2x^i}{d\lambda^2} = 0$$
Derive the geodesic equation for this metric. moore general relativity workbook solutions
Consider two clocks, one at rest at infinity and the other at rest at a distance $r$ from a massive object. Calculate the gravitational time dilation factor.
Derive the equation of motion for a radial geodesic. After some calculations, we find that the geodesic
$$\Gamma^0_{00} = 0, \quad \Gamma^i_{00} = 0, \quad \Gamma^i_{jk} = \eta^{im} \partial_m g_{jk}$$
$$\frac{d^2r}{d\lambda^2} = -\frac{GM}{r^2} \left(1 - \frac{2GM}{r}\right) \left(\frac{dt}{d\lambda}\right)^2 + \frac{GM}{r^2} \left(1 - \frac{2GM}{r}\right)^{-1} \left(\frac{dr}{d\lambda}\right)^2$$ After some calculations
Consider a particle moving in a curved spacetime with metric