This factor describes the difference in time measured by the two clocks.
where $\eta^{im}$ is the Minkowski metric. moore general relativity workbook solutions
$$\frac{d^2x^\mu}{d\lambda^2} + \Gamma^\mu_{\alpha\beta} \frac{dx^\alpha}{d\lambda} \frac{dx^\beta}{d\lambda} = 0$$ This factor describes the difference in time measured
$$\Gamma^0_{00} = 0, \quad \Gamma^i_{00} = 0, \quad \Gamma^i_{jk} = \eta^{im} \partial_m g_{jk}$$ \quad \Gamma^i_{00} = 0
Consider the Schwarzschild metric