where $\eta^{im}$ is the Minkowski metric.
$$\frac{d^2r}{d\lambda^2} = -\frac{GM}{r^2} \left(1 - \frac{2GM}{r}\right) \left(\frac{dt}{d\lambda}\right)^2 + \frac{GM}{r^2} \left(1 - \frac{2GM}{r}\right)^{-1} \left(\frac{dr}{d\lambda}\right)^2$$ moore general relativity workbook solutions
This factor describes the difference in time measured by the two clocks. where $\eta^{im}$ is the Minkowski metric
$$\frac{d^2r}{d\lambda^2} = -\frac{GM}{r^2} + \frac{L^2}{r^3}$$ moore general relativity workbook solutions
The geodesic equation is given by
Consider a particle moving in a curved spacetime with metric
The gravitational time dilation factor is given by