For the given metric, the non-zero Christoffel symbols are

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.

$$\frac{d^2x^\mu}{d\lambda^2} + \Gamma^\mu_{\alpha\beta} \frac{dx^\alpha}{d\lambda} \frac{dx^\beta}{d\lambda} = 0$$